IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Comparative study of a flexible and rigid two degree of freedom half car modeleSAT Journals
Abstract Ride quality is concerned with the feel of the passenger in the environment of a moving vehicle. It is one of the key indices in determining comfort levels of a vehicle. Although, “ride comfort” evaluation is subjective in nature, researchers have developed mathematical models to study and evaluate vehicle ride performance. Some popular models for vehicle ride analysis are – quarter car model, two dof (degree of freedom) and four dof half car model. These models model the chassis as a rigid body. This work removes this assumption and models the chassis of the vehicle as a flexible beam on a spring damper system at the front and rear using Euler beam theory. This elastic model has two dof – vehicle bounce and pitch, and has been compared with the rigid two dof model. Euler beam theory and Lagrangian mechanics are used to derive the equations of motion. Finite element method is used to validate this model. Experimental validation of the natural frequencies of this flexible beam is presented. Keywords: Flexible ride model, Elastic ride model
Design and analysis of x y- positioning stage based on redundant parallel li...eSAT Journals
Abstract This paper presents the concept of a planar positioning stage based on a kinematically redundant parallel linkage. Basic kinematics and workspace analysis of base redundant manipulator is initially explained and the procedure of static analysis to predict the actuated joint torques is described. As there are six actuators in the linkage, the redundancy can be overcome by proper selection of the base joint variables. Also it is assumed that the motion is at a constant speed. A numerical example is shown with a straight line trajectory to illustrate the workspace and joint force calculation aspects of this linkage. The possible arrangement of the stage with electrostatic actuation and sensing are finally highlighted. Keywords: Kinematic redundancy, Parallel mechanism, Static analysis, and Workspace characteristics
This document describes the design and analysis of a planar positioning stage based on a redundantly actuated parallel linkage. The positioning stage has three degrees of freedom (x-y-θ) and uses a 3-PRPR linkage with six actuators. The document analyzes the kinematics and workspace of the linkage. It describes the procedure for static analysis to calculate the actuated joint torques. The positioning stage could enable high-precision motion with a compact design and improved stiffness compared to serial linkages. It is proposed for potential use in micro-scale applications.
Dynamical modelling of the excavating chain of a ballast cleaning machineIJERA Editor
The ballast bed as part of the railway track fulfils the important functions as the binding element
between sleepers and substructure. Fouling increases over the years for various reasons. When the necessary
good functioning is no longer assured, ballast bed cleaning must be performed. The machines, that perform that
task, are equipped with various complex mechanics - hydraulic systems that ensure high productivity,
efficiency and quality of the works. In this article is presented one way of studying the work of the machine for
excavating ballast from the ballast bed to the sieving machine. We suggest a dynamic model for simulating the
work of a scraper chain of a ballast cleaning machine with different working parameters.
Signature analysis of cracked cantilever beamiaemedu
This document summarizes research on analyzing the vibration signature of a cracked cantilever beam through both simulation and experimentation. Finite element analysis was used to simulate the natural frequencies of cracked beams with varying crack depths and locations. Experimental testing was also conducted on physical cracked cantilever beams to obtain vibration signatures. The simulated and experimental natural frequency ratios were then compared for different crack scenarios in tables and plots. The results showed that vibration signature analysis can be used to detect cracks in beams by monitoring changes in natural frequencies.
Signature analysis of cracked cantilever beamiaemedu
This document summarizes research on analyzing the vibration signature of a cracked cantilever beam through both simulation and experimentation. Finite element analysis was used to simulate the natural frequencies of cracked beams with varying crack depths and locations. Experimental testing was also conducted on physical cracked cantilever beams to obtain vibration signatures. The simulated and experimental natural frequency ratios were then compared for different crack scenarios in tables and plots. The results showed that vibration signature analysis can be used to detect cracks in beams by monitoring changes in natural frequencies.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Improvement of energy absorption of thin walled hexagonal tube made of magnes...eSAT Journals
Abstract This paper describes potentially the using of magnesium alloy as an energy longitudinal member used in crashworthiness applications. Since magnesium alloys are lighter weight material, they are preferred to use to decrease the environmental pollution and fuel consumptions. Non-linear finite element was used to simulate the crash behaviour of the thin walled hexagonal tube. The tube was subjected to both direct and oblique loading. Trigger mechanism was applied in this study. The aim of using trigger is to decrease the initial peak load and to enhance the energy absorption capability of the tube and also crash force efficiency. Three trigger geometries have been applied circular, rectangular and elliptical geometry. Three type of trigger distribution already have been studied. The positions and the size of triggers are also investigated. It was found that the 10% per cent reductions with elliptical trigger revealed the best choice; it shows enhancing in energy absorption and CFE about10 per cent and decreasing in peak force by 10 per cent too.
Comparative study of a flexible and rigid two degree of freedom half car modeleSAT Journals
Abstract Ride quality is concerned with the feel of the passenger in the environment of a moving vehicle. It is one of the key indices in determining comfort levels of a vehicle. Although, “ride comfort” evaluation is subjective in nature, researchers have developed mathematical models to study and evaluate vehicle ride performance. Some popular models for vehicle ride analysis are – quarter car model, two dof (degree of freedom) and four dof half car model. These models model the chassis as a rigid body. This work removes this assumption and models the chassis of the vehicle as a flexible beam on a spring damper system at the front and rear using Euler beam theory. This elastic model has two dof – vehicle bounce and pitch, and has been compared with the rigid two dof model. Euler beam theory and Lagrangian mechanics are used to derive the equations of motion. Finite element method is used to validate this model. Experimental validation of the natural frequencies of this flexible beam is presented. Keywords: Flexible ride model, Elastic ride model
Design and analysis of x y- positioning stage based on redundant parallel li...eSAT Journals
Abstract This paper presents the concept of a planar positioning stage based on a kinematically redundant parallel linkage. Basic kinematics and workspace analysis of base redundant manipulator is initially explained and the procedure of static analysis to predict the actuated joint torques is described. As there are six actuators in the linkage, the redundancy can be overcome by proper selection of the base joint variables. Also it is assumed that the motion is at a constant speed. A numerical example is shown with a straight line trajectory to illustrate the workspace and joint force calculation aspects of this linkage. The possible arrangement of the stage with electrostatic actuation and sensing are finally highlighted. Keywords: Kinematic redundancy, Parallel mechanism, Static analysis, and Workspace characteristics
This document describes the design and analysis of a planar positioning stage based on a redundantly actuated parallel linkage. The positioning stage has three degrees of freedom (x-y-θ) and uses a 3-PRPR linkage with six actuators. The document analyzes the kinematics and workspace of the linkage. It describes the procedure for static analysis to calculate the actuated joint torques. The positioning stage could enable high-precision motion with a compact design and improved stiffness compared to serial linkages. It is proposed for potential use in micro-scale applications.
Dynamical modelling of the excavating chain of a ballast cleaning machineIJERA Editor
The ballast bed as part of the railway track fulfils the important functions as the binding element
between sleepers and substructure. Fouling increases over the years for various reasons. When the necessary
good functioning is no longer assured, ballast bed cleaning must be performed. The machines, that perform that
task, are equipped with various complex mechanics - hydraulic systems that ensure high productivity,
efficiency and quality of the works. In this article is presented one way of studying the work of the machine for
excavating ballast from the ballast bed to the sieving machine. We suggest a dynamic model for simulating the
work of a scraper chain of a ballast cleaning machine with different working parameters.
Signature analysis of cracked cantilever beamiaemedu
This document summarizes research on analyzing the vibration signature of a cracked cantilever beam through both simulation and experimentation. Finite element analysis was used to simulate the natural frequencies of cracked beams with varying crack depths and locations. Experimental testing was also conducted on physical cracked cantilever beams to obtain vibration signatures. The simulated and experimental natural frequency ratios were then compared for different crack scenarios in tables and plots. The results showed that vibration signature analysis can be used to detect cracks in beams by monitoring changes in natural frequencies.
Signature analysis of cracked cantilever beamiaemedu
This document summarizes research on analyzing the vibration signature of a cracked cantilever beam through both simulation and experimentation. Finite element analysis was used to simulate the natural frequencies of cracked beams with varying crack depths and locations. Experimental testing was also conducted on physical cracked cantilever beams to obtain vibration signatures. The simulated and experimental natural frequency ratios were then compared for different crack scenarios in tables and plots. The results showed that vibration signature analysis can be used to detect cracks in beams by monitoring changes in natural frequencies.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Improvement of energy absorption of thin walled hexagonal tube made of magnes...eSAT Journals
Abstract This paper describes potentially the using of magnesium alloy as an energy longitudinal member used in crashworthiness applications. Since magnesium alloys are lighter weight material, they are preferred to use to decrease the environmental pollution and fuel consumptions. Non-linear finite element was used to simulate the crash behaviour of the thin walled hexagonal tube. The tube was subjected to both direct and oblique loading. Trigger mechanism was applied in this study. The aim of using trigger is to decrease the initial peak load and to enhance the energy absorption capability of the tube and also crash force efficiency. Three trigger geometries have been applied circular, rectangular and elliptical geometry. Three type of trigger distribution already have been studied. The positions and the size of triggers are also investigated. It was found that the 10% per cent reductions with elliptical trigger revealed the best choice; it shows enhancing in energy absorption and CFE about10 per cent and decreasing in peak force by 10 per cent too.
The Effect of Arm Stiffness on the Elasto-Kinematic Properties of Single-Axle...theijes
The paper is focused on the stiffness analysis of the longitudinal arm of single-axle suspension on elastokinematic behaviour of the vehicle axle which is highly important when considering the handling characteristics related tovehicle safety.The elasto-kinematic behaviour of the axle determines the course of the geometrical parameters of wheel suspension, the toe angle and camber as the function of wheel movement during force loading. This paper presents the complex MBS (Multi-Body Simulation)model of the wheel suspension with nonlinear characteristics of rubber-metal bushings. The model also comprises force elements such as springs, shock absorbers, stops and the transverse stabilizer. The model of flexible arm is implemented in the MBS model using the Craig-Bampton method, which represents a flexible body based on the synthesis of its own modal shapes. Subsequently,elasto-kinematic simulations are performed with the help ofthe computational system Hyperwork. The computational part of the paper presents the results of the elasto-kinematic behaviour of wheel axle for the flexible arm with different sheet metal thicknesses (2, 3 and 4 mm) and different materials (steel and aluminium alloy AlSi7Mg). Individual calculation models are compared to each other and also to the model of suspension with therigidarm. Elasto-kinematic analyses are also validated by the measurement inthe testing stage.
Sale (2013) Structural Optimization of Composite Blades for Wind and Hydrokin...Danny Sale
This document describes research into developing a numerical methodology for structural analysis and optimization of composite wind and hydrokinetic turbine blades. It presents a simplified structural model based on classical lamination theory and beam theory, suitable for design optimization. The document outlines validating this model and formulating an optimization problem to minimize blade mass under stress, deflection and frequency constraints. It demonstrates the optimization methodology by designing a composite hydrokinetic turbine blade, comparing optimization algorithms, and analyzing effects of uncertain material properties on structural performance.
A METHODOLOGY FOR ANALYSIS OF TOPOLOGICAL CHARATERISTICS OF PLANETARY GEAR TR...meijjournal
A planetary trains for multi-speed is mainly used for automation in industries of automobile. A planetary
gear train is represented by a graph. It is identified by (i) number of vertices and their connectivity (ii)
number of edges and their types and values (iii) fundamental circuits, their size and adjancy. Connectivity
of individual link is a property characteristic of kinematic chain. It is possible to identify a planetary gear,
therefore of using sets of labele (decimal numbers representing connectivity ) of individual link. The
connectivity of vertices , edges values and circuit values, related to design invariants which in turn
indicates the possible behavior of the gear train ( for example capacity of power transmission, speed ratio
and power carculation). For a specified degree – of – freedom a number of planetary gear kinematic chain
(PGKCs) are selected and hence planetary gear trains (PGTs) can be formed with a given number of links
and joints so that designer must be able to select to select the best train from the view point of say velocity
ratio and capacity of power transmission, space requirements etc. Synthesis of planetary gear kinematic
chain and planetary gear trains has been studied(1-9). Almost all reported work deals with only
identification of distinct chains. Besides providing an atlus of chains, this in itself does not provide any help
to designer in the selection of best possible gear train. In the present paper a simple method based of
circuit property ( based on link-link shortest path distance and degree of links) is presented to determine
the topology values of power transmission efficiency and topology power transmission capacity of five-links
PGKCs and their distinct inversions.
This document presents a monolithic bistable mechanism that does not rely on residual stress. It consists of two curved beams clamped at the center.
Analytic and finite element modeling is used to predict and design the bistable behavior. The modeling shows that for a single curved beam to be bistable, its second buckling mode must be constrained. A double curved beam structure satisfies this requirement through mutual cancellation of twisting modes.
Microfabricated double curved beam tests match the analytic predictions well. The design allows tailoring of the bistable behavior without needing residual stress or complex structures.
My Amazing CFD Coursework - Competitiveness of the Ferrari F2002Nadezda Avanessova
This report analyzes the aerodynamics of the Ferrari F2002 race car and compares it to winners of 2016-2017 seasons using computational fluid dynamics simulations. The Ferrari F2002 geometry was imported and its mesh was refined. A k-epsilon turbulence model was used to simulate the turbulent, incompressible flow. Simulation results found the F2002 generated 1560N of downforce at 57.2m/s, which would likely be sufficient to compete with modern cars. However, in an overtaking simulation downforce dropped significantly, indicating performance may decrease in traffic. Preliminary results for a Mercedes also showed higher downforce, suggesting it may have better handling.
—This paper presents a new image based visual servoing (IBVS) control scheme for omnidirectional wheeled mobile robots with four swedish wheels. The contribution is the proposal of a scheme that consider the overall dynamic of the system; this means, we put together mechanical and electrical dynamics. The actuators are direct current (DC) motors, which imply that the system input signals are armature voltage applied to DC motors. In our control scheme the PD control law and eye-to-hand camera configuration are used to compute the armature voltages and to measure system states, respectively. Stability proof is performed via Lypunov direct method and LaSalle's invariance principle. Simulation and experimental results were performed in order to validate the theoretical proposal and to show the good performance of the posture errors. Keywords—IBVS, posture control, omnidirectional wheeled mobile robot, dynamic actuator, Lyapunov direct method.
The document discusses digital manufacturing tools including generative design, reverse engineering, additive manufacturing, and communicating design. For generative design, it describes goal seeking and optimization techniques, noting limitations include multi-objective optimization, complex constraints, and manufacturability. For reverse engineering, it summarizes common 3D file formats like STL, OBJ, FBX, and 3DS used to capture geometry and textures. For additive manufacturing, it discusses 3D printing processes. And for communicating design, it mentions file sharing platforms and virtual/augmented reality.
1) The document describes the modeling of an active magnetic bearing control system using finite element analysis.
2) A dynamic model of the active magnetic bearing was developed using ordinary differential equations to describe the electrical behavior of the windings and mechanical behavior of the magnetically suspended shaft.
3) Finite element analysis was used to compute the magnetic field distribution and determine properties of the magnetic bearing actuator like current and position stiffness coefficients.
Kinematics Analysis of Parallel Mechanism Based on Force Feedback DeviceIJRES Journal
Kinematic analysis of mechanism is the fundamental work of force feedback device research.The
composition of Delta mechanism based on Omega.7 force feedback device was illustrated in this paper.The
kinematic loop equations of Delta mechanism was established according to its geometric relationship,also the
inverse kinematics solution of Delta mechanism were obtained. And the numerical forward kinematics were
calculated by Newton iteration algorithm.Finally,The analysis of velocity and acceleration was carried out
through matrix operations.Kinematic analysis of Delta mechanism provides a theoretical basis for following
study.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Research regarding calculation of the tensile forces of polyurethane film and...eSAT Journals
Abstract In this paper it is analyzed in terms of kinematics and mechanical, stress occurring in protective paper all the way. It will be analyzed forces and tensions that arise in paper strip in the stretch area, stretching determining race. It follows determination of a continuous tension in the paper strip to optimize the operation Keywords: paper route, tension, polyurethane
On the Performances Investigation of Different Surface Mounted Permanent Magn...IAES-IJPEDS
In recent years, permanent magnet machines have become a common choice
in many industrial applications. Therefore, several structures have been
developed, and the choice of a topology designed for a specified application
requires the knowledge of the advantages and disadvantages of different
topologies. The present work deals with the evaluation of the performances
of different radial flux surface-mounted permanent magnet motors designed
for an electric vehicle motor application. The objective of this survey is to
show the effect of the rotor position (inner or outer) and the magnets
segmentation on the machine output torque and iron losses. In this context,
four machines with: (i) inner rotor, (ii) inner rotor segmented magnets, (iii)
outer rotor and (iv) outer rotor segmented magnets have been designed and
studied. All these machines have the same geometrical dimensions and
current loading. The main idea is to develop a machine with smoothness
torque, lower torque ondulation, lower iron losses, and which is mechanically
robust. Firstly, the output torque of the different structure is computed.
Secondly, by means of an improved analytical model coupled with 2
dimensional transient finite element analysis (FEA), the machines iron losses
are predicted.
A Novel Hybrid Approach for Stability Analysis of SMIB using GA and PSOINFOGAIN PUBLICATION
This document presents a hybrid approach for stability analysis of a single machine infinite bus system (SMIB) using a generic power system stabilizer (GPSS), proportional-integral-derivative (PID) controller, and genetic algorithm (GA) or particle swarm optimization (PSO). It first describes the mathematical models and equations for modeling an SMIB system. It then discusses GPSS and PID controllers for stabilizing an SMIB. A hybrid approach is proposed that uses both GPSS and PID to reduce spikes in the GPSS output. Simulation results show the rotor and phase angle deviations for different controllers, and compare the proposed hybrid GA and PSO approaches to other methods.
OPTIMIZATION OF AERODYNAMIC AND STRUCTURAL PERFORMANCES OF A WIND TURBINE BLA...IAEME Publication
The purpose of this study is to optimize the energy efficiency of a wind turbine
blade and reduce its cost. In this paper, we define several optimization targets such as
maximizing Cl / Cd ratio and minimizing the deformation and mass of the blade. To
solve this multi-objectives optimization problem, we used the ant colony heuristic
optimization method on a blade model computed by the BEM and the FEM methods.
The optimization results are compared with the results obtained by the BEM method.
IRJET- VLSI Architecture for Montgomery Modular MultiplicationIRJET Journal
The document discusses several VLSI architectures for Montgomery modular multiplication (MM) algorithms used in public key cryptography. It compares the performance of four MM multiplier designs: Radix-2 Montgomery, SCS-based Montgomery, FCS-based Montgomery, and a modified SCS-based Montgomery. The modified SCS design aims to reduce critical path delay while maintaining low hardware complexity. It was implemented on an FPGA and achieved a delay of 3.59ns, power of 20.36mW, and frequency of 278MHz, showing improvements over the other designs.
Topology Optimization of Gears from Two Wheeler Gear Set Using Parametric StudyIOSRJMCE
: Gears are used to transmit motion from on shaft to another and it has wide variety of applications. One of the applications of gear is in automobile gear box. Gears generally fail when the working stress exceeds the maximum permissible stress. These stresses are proportional to the amount of power transmitted by the gears. This project intends to identify the magnitude of the stresses for a given configuration of a two wheeler gears transmitting power while trying to find ways for reducing weight of the gear. The philosophy for driving this work is the lightness of the gear for a given purpose while keeping intact its functionality thus reducing the material cost of the gear. Ease of incorporating the new feature for weight reduction over the existing process of manufacturing and the magnitude of volume of weight reduced could be considered as the key parameters for assessment for this work.
Unguided crack growth simulation in asymmetric specimens using bond-based per...IRJET Journal
This document summarizes a study that uses peridynamics, a nonlocal continuum theory, to simulate unguided crack growth in asymmetric specimens. The study develops peridynamic simulations of pre-cracked plates containing asymmetric circular notches subjected to tension. Various models are analyzed with different notch positions and numbers. The results show that peridynamics can successfully predict complex crack patterns, including curved crack growth paths and cracks initiating from the notches. The study demonstrates that peridynamics is a promising technique for fracture analysis of structures with asymmetries.
This document presents a model called the Improved Fault Location Model (IFLM) to determine fault location and fault voltage on a long transmission line of 200 miles (320 km). The IFLM uses impedance matrix analysis and unit current injections to calculate the bus impedance matrix of the line. Measurement of voltages at the two line ends are used along with the bus impedance matrix calculations to determine equations relating the fault location, fault voltage, and measured voltage changes due to the fault. By solving these equations, the fault location and voltage can be estimated without requiring fault currents, which are not always available from measurements.
This document presents a mathematical model and analysis of the vibration response characteristics of a half car model subjected to different sinusoidal road excitations. The half car model is modeled as a two degree of freedom system, considering bounce and pitch motions. Lagrange's equations are used to derive the governing equations of motion. The natural frequencies of the system are calculated. MATLAB is used to simulate the dynamic response of the vehicle for different road bump amplitudes and vehicle velocities. The results show that vibration amplitude increases with bump amplitude and velocity up to a point, after which amplitude decreases with further increases in velocity.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
The Effect of Arm Stiffness on the Elasto-Kinematic Properties of Single-Axle...theijes
The paper is focused on the stiffness analysis of the longitudinal arm of single-axle suspension on elastokinematic behaviour of the vehicle axle which is highly important when considering the handling characteristics related tovehicle safety.The elasto-kinematic behaviour of the axle determines the course of the geometrical parameters of wheel suspension, the toe angle and camber as the function of wheel movement during force loading. This paper presents the complex MBS (Multi-Body Simulation)model of the wheel suspension with nonlinear characteristics of rubber-metal bushings. The model also comprises force elements such as springs, shock absorbers, stops and the transverse stabilizer. The model of flexible arm is implemented in the MBS model using the Craig-Bampton method, which represents a flexible body based on the synthesis of its own modal shapes. Subsequently,elasto-kinematic simulations are performed with the help ofthe computational system Hyperwork. The computational part of the paper presents the results of the elasto-kinematic behaviour of wheel axle for the flexible arm with different sheet metal thicknesses (2, 3 and 4 mm) and different materials (steel and aluminium alloy AlSi7Mg). Individual calculation models are compared to each other and also to the model of suspension with therigidarm. Elasto-kinematic analyses are also validated by the measurement inthe testing stage.
Sale (2013) Structural Optimization of Composite Blades for Wind and Hydrokin...Danny Sale
This document describes research into developing a numerical methodology for structural analysis and optimization of composite wind and hydrokinetic turbine blades. It presents a simplified structural model based on classical lamination theory and beam theory, suitable for design optimization. The document outlines validating this model and formulating an optimization problem to minimize blade mass under stress, deflection and frequency constraints. It demonstrates the optimization methodology by designing a composite hydrokinetic turbine blade, comparing optimization algorithms, and analyzing effects of uncertain material properties on structural performance.
A METHODOLOGY FOR ANALYSIS OF TOPOLOGICAL CHARATERISTICS OF PLANETARY GEAR TR...meijjournal
A planetary trains for multi-speed is mainly used for automation in industries of automobile. A planetary
gear train is represented by a graph. It is identified by (i) number of vertices and their connectivity (ii)
number of edges and their types and values (iii) fundamental circuits, their size and adjancy. Connectivity
of individual link is a property characteristic of kinematic chain. It is possible to identify a planetary gear,
therefore of using sets of labele (decimal numbers representing connectivity ) of individual link. The
connectivity of vertices , edges values and circuit values, related to design invariants which in turn
indicates the possible behavior of the gear train ( for example capacity of power transmission, speed ratio
and power carculation). For a specified degree – of – freedom a number of planetary gear kinematic chain
(PGKCs) are selected and hence planetary gear trains (PGTs) can be formed with a given number of links
and joints so that designer must be able to select to select the best train from the view point of say velocity
ratio and capacity of power transmission, space requirements etc. Synthesis of planetary gear kinematic
chain and planetary gear trains has been studied(1-9). Almost all reported work deals with only
identification of distinct chains. Besides providing an atlus of chains, this in itself does not provide any help
to designer in the selection of best possible gear train. In the present paper a simple method based of
circuit property ( based on link-link shortest path distance and degree of links) is presented to determine
the topology values of power transmission efficiency and topology power transmission capacity of five-links
PGKCs and their distinct inversions.
This document presents a monolithic bistable mechanism that does not rely on residual stress. It consists of two curved beams clamped at the center.
Analytic and finite element modeling is used to predict and design the bistable behavior. The modeling shows that for a single curved beam to be bistable, its second buckling mode must be constrained. A double curved beam structure satisfies this requirement through mutual cancellation of twisting modes.
Microfabricated double curved beam tests match the analytic predictions well. The design allows tailoring of the bistable behavior without needing residual stress or complex structures.
My Amazing CFD Coursework - Competitiveness of the Ferrari F2002Nadezda Avanessova
This report analyzes the aerodynamics of the Ferrari F2002 race car and compares it to winners of 2016-2017 seasons using computational fluid dynamics simulations. The Ferrari F2002 geometry was imported and its mesh was refined. A k-epsilon turbulence model was used to simulate the turbulent, incompressible flow. Simulation results found the F2002 generated 1560N of downforce at 57.2m/s, which would likely be sufficient to compete with modern cars. However, in an overtaking simulation downforce dropped significantly, indicating performance may decrease in traffic. Preliminary results for a Mercedes also showed higher downforce, suggesting it may have better handling.
—This paper presents a new image based visual servoing (IBVS) control scheme for omnidirectional wheeled mobile robots with four swedish wheels. The contribution is the proposal of a scheme that consider the overall dynamic of the system; this means, we put together mechanical and electrical dynamics. The actuators are direct current (DC) motors, which imply that the system input signals are armature voltage applied to DC motors. In our control scheme the PD control law and eye-to-hand camera configuration are used to compute the armature voltages and to measure system states, respectively. Stability proof is performed via Lypunov direct method and LaSalle's invariance principle. Simulation and experimental results were performed in order to validate the theoretical proposal and to show the good performance of the posture errors. Keywords—IBVS, posture control, omnidirectional wheeled mobile robot, dynamic actuator, Lyapunov direct method.
The document discusses digital manufacturing tools including generative design, reverse engineering, additive manufacturing, and communicating design. For generative design, it describes goal seeking and optimization techniques, noting limitations include multi-objective optimization, complex constraints, and manufacturability. For reverse engineering, it summarizes common 3D file formats like STL, OBJ, FBX, and 3DS used to capture geometry and textures. For additive manufacturing, it discusses 3D printing processes. And for communicating design, it mentions file sharing platforms and virtual/augmented reality.
1) The document describes the modeling of an active magnetic bearing control system using finite element analysis.
2) A dynamic model of the active magnetic bearing was developed using ordinary differential equations to describe the electrical behavior of the windings and mechanical behavior of the magnetically suspended shaft.
3) Finite element analysis was used to compute the magnetic field distribution and determine properties of the magnetic bearing actuator like current and position stiffness coefficients.
Kinematics Analysis of Parallel Mechanism Based on Force Feedback DeviceIJRES Journal
Kinematic analysis of mechanism is the fundamental work of force feedback device research.The
composition of Delta mechanism based on Omega.7 force feedback device was illustrated in this paper.The
kinematic loop equations of Delta mechanism was established according to its geometric relationship,also the
inverse kinematics solution of Delta mechanism were obtained. And the numerical forward kinematics were
calculated by Newton iteration algorithm.Finally,The analysis of velocity and acceleration was carried out
through matrix operations.Kinematic analysis of Delta mechanism provides a theoretical basis for following
study.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Research regarding calculation of the tensile forces of polyurethane film and...eSAT Journals
Abstract In this paper it is analyzed in terms of kinematics and mechanical, stress occurring in protective paper all the way. It will be analyzed forces and tensions that arise in paper strip in the stretch area, stretching determining race. It follows determination of a continuous tension in the paper strip to optimize the operation Keywords: paper route, tension, polyurethane
On the Performances Investigation of Different Surface Mounted Permanent Magn...IAES-IJPEDS
In recent years, permanent magnet machines have become a common choice
in many industrial applications. Therefore, several structures have been
developed, and the choice of a topology designed for a specified application
requires the knowledge of the advantages and disadvantages of different
topologies. The present work deals with the evaluation of the performances
of different radial flux surface-mounted permanent magnet motors designed
for an electric vehicle motor application. The objective of this survey is to
show the effect of the rotor position (inner or outer) and the magnets
segmentation on the machine output torque and iron losses. In this context,
four machines with: (i) inner rotor, (ii) inner rotor segmented magnets, (iii)
outer rotor and (iv) outer rotor segmented magnets have been designed and
studied. All these machines have the same geometrical dimensions and
current loading. The main idea is to develop a machine with smoothness
torque, lower torque ondulation, lower iron losses, and which is mechanically
robust. Firstly, the output torque of the different structure is computed.
Secondly, by means of an improved analytical model coupled with 2
dimensional transient finite element analysis (FEA), the machines iron losses
are predicted.
A Novel Hybrid Approach for Stability Analysis of SMIB using GA and PSOINFOGAIN PUBLICATION
This document presents a hybrid approach for stability analysis of a single machine infinite bus system (SMIB) using a generic power system stabilizer (GPSS), proportional-integral-derivative (PID) controller, and genetic algorithm (GA) or particle swarm optimization (PSO). It first describes the mathematical models and equations for modeling an SMIB system. It then discusses GPSS and PID controllers for stabilizing an SMIB. A hybrid approach is proposed that uses both GPSS and PID to reduce spikes in the GPSS output. Simulation results show the rotor and phase angle deviations for different controllers, and compare the proposed hybrid GA and PSO approaches to other methods.
OPTIMIZATION OF AERODYNAMIC AND STRUCTURAL PERFORMANCES OF A WIND TURBINE BLA...IAEME Publication
The purpose of this study is to optimize the energy efficiency of a wind turbine
blade and reduce its cost. In this paper, we define several optimization targets such as
maximizing Cl / Cd ratio and minimizing the deformation and mass of the blade. To
solve this multi-objectives optimization problem, we used the ant colony heuristic
optimization method on a blade model computed by the BEM and the FEM methods.
The optimization results are compared with the results obtained by the BEM method.
IRJET- VLSI Architecture for Montgomery Modular MultiplicationIRJET Journal
The document discusses several VLSI architectures for Montgomery modular multiplication (MM) algorithms used in public key cryptography. It compares the performance of four MM multiplier designs: Radix-2 Montgomery, SCS-based Montgomery, FCS-based Montgomery, and a modified SCS-based Montgomery. The modified SCS design aims to reduce critical path delay while maintaining low hardware complexity. It was implemented on an FPGA and achieved a delay of 3.59ns, power of 20.36mW, and frequency of 278MHz, showing improvements over the other designs.
Topology Optimization of Gears from Two Wheeler Gear Set Using Parametric StudyIOSRJMCE
: Gears are used to transmit motion from on shaft to another and it has wide variety of applications. One of the applications of gear is in automobile gear box. Gears generally fail when the working stress exceeds the maximum permissible stress. These stresses are proportional to the amount of power transmitted by the gears. This project intends to identify the magnitude of the stresses for a given configuration of a two wheeler gears transmitting power while trying to find ways for reducing weight of the gear. The philosophy for driving this work is the lightness of the gear for a given purpose while keeping intact its functionality thus reducing the material cost of the gear. Ease of incorporating the new feature for weight reduction over the existing process of manufacturing and the magnitude of volume of weight reduced could be considered as the key parameters for assessment for this work.
Unguided crack growth simulation in asymmetric specimens using bond-based per...IRJET Journal
This document summarizes a study that uses peridynamics, a nonlocal continuum theory, to simulate unguided crack growth in asymmetric specimens. The study develops peridynamic simulations of pre-cracked plates containing asymmetric circular notches subjected to tension. Various models are analyzed with different notch positions and numbers. The results show that peridynamics can successfully predict complex crack patterns, including curved crack growth paths and cracks initiating from the notches. The study demonstrates that peridynamics is a promising technique for fracture analysis of structures with asymmetries.
This document presents a model called the Improved Fault Location Model (IFLM) to determine fault location and fault voltage on a long transmission line of 200 miles (320 km). The IFLM uses impedance matrix analysis and unit current injections to calculate the bus impedance matrix of the line. Measurement of voltages at the two line ends are used along with the bus impedance matrix calculations to determine equations relating the fault location, fault voltage, and measured voltage changes due to the fault. By solving these equations, the fault location and voltage can be estimated without requiring fault currents, which are not always available from measurements.
This document presents a mathematical model and analysis of the vibration response characteristics of a half car model subjected to different sinusoidal road excitations. The half car model is modeled as a two degree of freedom system, considering bounce and pitch motions. Lagrange's equations are used to derive the governing equations of motion. The natural frequencies of the system are calculated. MATLAB is used to simulate the dynamic response of the vehicle for different road bump amplitudes and vehicle velocities. The results show that vibration amplitude increases with bump amplitude and velocity up to a point, after which amplitude decreases with further increases in velocity.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Study of macro mechanical properties of ultra high strength concrete using qu...eSAT Publishing House
The document discusses a study on developing ultra-high strength concrete (UHSC) using locally available materials to achieve a compressive strength over 180 MPa. Various mixes were tested with different percentages of quartz powder (30-45%) and curing methods including normal water curing and hot air curing at 200°C for 1-3 days. The results showed that compressive strength increased up to 187 MPa for mixes with 40% quartz powder that were hot air cured for 1 day, compared to 116 MPa for normal water curing only. Higher quartz powder content and thermal curing improved strength through increased packing density and hydration reactions.
Compressive strength variability of brown coal fly ash geopolymer concreteeSAT Publishing House
The document summarizes research investigating the compressive strength variability of geopolymer concrete made with brown coal fly ash as a binder. Testing of six mixes of geopolymer concrete found a large range in 28-day compressive strengths, from 43.81 MPa to 7.21 MPa. Additional chemical analysis found significant variability in the chemical composition of samples from the same brown coal fly ash source, particularly in the silicon dioxide and aluminum oxide contents. This variability is believed to contribute to the variability in compressive strengths and suggests the need for pretreatment and refinement of brown coal fly ash to produce more consistent geopolymer concrete.
Economical placement of shear walls in a moment resisting frame for earthquak...eSAT Publishing House
This document analyzes different configurations of shear wall placement in a 5-story reinforced concrete building to determine the optimal configuration for earthquake resistance. Five frames with different shear wall layouts are modeled and analyzed. Frame 2, with shear walls at the building core, performed best with significant reductions in lateral displacement, bending moment, shear force, and axial force compared to the frame without shear walls. For economic feasibility, the top 1-2 stories were removed from Frames 2 and 3. This curtailment further reduced lateral displacement, inter-story drift, bending moment, and shear force, particularly for Frames 7-9. In conclusion, curtailing the top 1-2 stories of Frames 2 or 3 provided the best
Effect of chemical treatments on the characteristics of regular and compact c...eSAT Publishing House
1) The document examines the effects of various chemical treatments (scouring, bleaching, mercerizing, dyeing) on the physical properties of regular and compact cotton spun yarns.
2) Testing showed that chemical treatments generally increased yarn tenacity but decreased elongation. Work of rupture was higher for slack mercerized yarns.
3) Bleached yarns showed poorer abrasion resistance while other treated yarns did not change. All treatments increased yarn friction. Slack mercerization significantly increased shrinkage for both yarn types.
Review on tls or ssl session sharing based web cluster load balancingeSAT Publishing House
This document summarizes a research paper that proposes a new technique for improving load balancing and performance in TLS/SSL web clusters. The technique shares TLS/SSL sessions across servers in the cluster so that if a client reconnects, the session can be reused without renegotiating. This saves time compared to establishing a new session. The document outlines how TLS/SSL works, how traditional load balancing can degrade performance under high loads, and how the proposed technique of sharing sessions within a cluster improves requests per second by 40-60% compared to no session sharing. It also compares the new technique to using SSL with backend forwarding and finds it reduces latency by 40% and improves throughput.
Factors affecting def and asr in the concrete dam at vrané nad vltavoueSAT Publishing House
1) The document examines factors affecting delayed ettringite formation (DEF) and alkali-silica reaction (ASR) in concrete from a dam in Vrané nad Vltavou, Czech Republic.
2) Samples were taken from 8 locations and tested for residual expansion, then analyzed using microscopy techniques. The sample with the highest residual expansion and microcracking was periodically exposed to water.
3) DEF was found to be the primary degradation mechanism. The sample most affected was located 1 meter above the water line and contained aggregates of acidic volcanic rock that are susceptible to DEF when periodically exposed to water.
Harmonized scheme for data mining technique to progress decision support syst...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
This document presents a model of parallel unit-connected generators to study the influence on third harmonic stator ground fault protection. Circuit models of the generators under normal and fault conditions are developed. Mesh analysis is used to obtain equations relating the third harmonic voltages and currents, which are solved using Cramer's rule. Simulations are performed in MATLAB/SIMULINK to validate the models and study the third harmonic voltage characteristics at the stator neutral and terminal for different fault locations and generator loading conditions. The analysis determines how the third harmonic voltages vary between the normal and faulted states, and how this affects the application of third harmonic protection for the parallel unit connection.
An innovative way for computerized smith chart generation and transmission li...eSAT Publishing House
This document describes a computer program that was developed to generate and interact with the Smith chart, a graphical tool used to solve transmission line problems. The program allows users to input transmission line parameters and see how they are represented on the Smith chart. It then demonstrates how to use the program to solve common transmission line problems by calculating reflection coefficients, impedances, admittances, and stub locations. The program is intended to help explain concepts of the Smith chart to students in an interactive way using a computer.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document summarizes an experimental study on velocity control of a hydraulic cylinder using an electro-hydraulic servo system. The system uses either a variable displacement axial piston pump controlled by a swashplate, or a proportional valve, to control the velocity of the cylinder. Mathematical models of the pump, valve, cylinder and external loads are developed. A PID controller is implemented to achieve constant velocity control under varying external loads. Experimental results show the PID controller can achieve good velocity control using either the variable pump or proportional valve under changing load conditions.
This document discusses computational fluid dynamics (CFD) analysis of flow over an airfoil integrated with spikes at supersonic speeds. It presents the results of CFD simulations using ANSYS Fluent software to analyze the effect of adding either a sharp spike or hemispherical spike to a NACA 651-412 airfoil at Mach numbers over 1. The study found that the addition of spikes modifies the flow field over the airfoil and changes the aerodynamic lift and drag coefficients. Spikes help reduce problems like higher heating and separation that occur during supersonic flight.
Application of ibearugbulem’s model for optimizing granite concrete mixeSAT Publishing House
This document presents a mathematical model for predicting the compressive strength of granitic concrete using Ibearugbulem's regression model. 45 concrete cubes were cast using different mix ratios and tested to determine compressive strength. The first 11 mixes were used to determine the regression model coefficients, and the full 15 mixes were used to validate the model. A t-test found the model results adequately predicted the experimental compressive strengths at a 95% confidence level. The developed model can predict compressive strength or mix proportions for granitic concrete given one is known.
Placate packet dropping attack using secure routing protocol and incentive ba...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document presents an investigation of the behavior of 3 degree of freedom spring mass damper systems subjected to transient loads. Two models of the spring mass damper system are modeled and their governing equations are derived. The velocities of the oscillators are estimated by solving the governing equations for a loss factor of 0.15. The kinetic and potential energies are calculated using the mass, velocity and stiffness of the oscillators to estimate the total energy. It is found that when the load changes from full to partial over time, there is a significant increase in displacement and velocity, dissipating more energy.
This document discusses investigating the behavior of a 3 degree of freedom spring mass damper system subjected to transient loads. It presents two models of the system with different damper configurations and derives the governing equations. The velocities and energies (kinetic and potential) of the oscillators are estimated by solving the equations for an exponential decaying, constant, and partial load over time. The results show the contribution of kinetic energy is minimal for oscillator 2 in all cases, while potential energy and contributions from oscillators 1 and 3 depend on the load type.
This document describes the design and analysis of a planar positioning stage based on a redundantly actuated parallel linkage with six degrees of freedom (three translations and three rotations). The kinematics and workspace analysis of the linkage are presented. A static analysis method to calculate the actuator torques required for a given end-effector force and trajectory is also described. MATLAB programs were developed to analyze the workspace and perform the static analysis. The results show that the redundant actuation can help improve the workspace characteristics and prevent singular configurations compared to non-redundant parallel manipulators. The stage design has potential applications in micro-positioning.
The active suspension system with hydraulic actuator for half car model analy...eSAT Publishing House
This document describes the design and simulation of an active suspension system with a hydraulic actuator for a half car model. A PID controller is designed and tuned using three different methods - heuristic tuning, Ziegler-Nichols tuning, and iterative learning algorithm tuning. The half car model and hydraulic actuator are modeled and simulated in MATLAB Simulink. Simulation results show that the PID controller tuned with the iterative learning algorithm provides the best ride quality performance compared to the other tuning methods or a passive suspension, reducing the body displacement under various road disturbances.
IRJET- Analysis and Design of Bridge Deck using Grillage Method - As Per IRCIRJET Journal
This document summarizes the analysis and design of a bridge deck using the grillage method according to IRC standards. It discusses modeling the bridge deck as a grillage of beams in Staad Pro software to represent the stiffness of the actual deck. Loads including self-weight, wearing coat, footpath live load, and vehicular live loads are applied to the grillage model. Linear static analysis is performed to determine bending moments and shear forces. The maximum bending moment of 464 kNm and maximum shear force of 316 kN occur under a 70R tracked vehicle based on IRC impact factors. The grillage method provides accurate results for bridge analysis if member properties are properly specified.
This document summarizes a methodology for sizing mechatronic systems using bond graphs and genetic algorithms. It proposes using bond graphs to develop structural models that satisfy control criteria like controllability and observability. Behavioral models are derived from the bond graph models. Genetic algorithms are then used to optimize the bond graph elements, with controllability and observability gramians as the fitness function. The method is demonstrated by applying it to size resistance (R) and capacitance (C) elements in a bond graph model of an automatic scooter transmission. Optimization yields values of 0.4227 for R and 0.3132 for C. Validation involves dynamic simulation to compare the sized model against the initial model.
Bond graphs and genetic algorithms for design and optimization of active dyna...eSAT Journals
Abstract The aim of this work is to propose a methodology of sizing in a frame of the conception of mechatronic systems in particular and active dynamic ones, in general. This methodology will support conceptual design step [1]. We propose a collaborative design approach based on Bond Graph tool and Genetic algorithms. Mechatronic systems have a passive part and active part. In our approach we establish a hard interaction between passive and active parts. This interaction will be materialized in taking into account of control criteria in the evolution (synthesis) phase of passive part. This initiative treats functional aspects, both structural and behavioral; while respecting interactions between passive and active parts. In our approach we treat functional, structural and behavioral aspects in order to validate a post-project solution. Optimization needs Behavioral models which are systematically deducted from bond-graph structural models. Thus, retained bond graph elements which constitute passive part will be obtained, done by optimization Genetic Algorithms procedure. In this procedure Gramians of controllability and of observability represent the fitness function. The proposed method will be applied to an automatic transmission of a scooter and validated by a dynamic simulation. Keywords: Modeling, dynamic system, Bond graph, Gramians of controllability, Genetic algorithms
Experimental investigation on circular hollow steel columns in filled with li...eSAT Journals
Abstract
Composite Circular hollow Steel tubes with and without GFRP infill for three different grades of Light weight concrete are tested for
ultimate load capacity and axial shortening , under Cyclic loading. Steel tubes are compared for different lengths, cross sections and
thickness. Specimens were tested separately after adopting Taguchi’s L9 (Latin Squares) Orthogonal array in order to save the initial
experimental cost on number of specimens and experimental duration. Analysis was carried out using ANN (Artificial Neural
Network) technique with the assistance of Mini Tab- a statistical soft tool. Comparison for predicted, experimental & ANN output is
obtained from linear regression plots. From this research study, it can be concluded that *Cross sectional area of steel tube has most
significant effect on ultimate load carrying capacity, *as length of steel tube increased- load carrying capacity decreased & *ANN
modeling predicted acceptable results. Thus ANN tool can be utilized for predicting ultimate load carrying capacity for composite
columns.
Keywords: Light weight concrete, GFRP, Artificial Neural Network, Linear Regression, Back propagation, orthogonal
Array, Latin Squares
This document summarizes an experimental investigation on circular hollow steel columns infilled with lightweight concrete, with and without glass fiber reinforced polymer (GFRP), under cyclic loading. Specimens of different steel tube lengths, cross-sections, thicknesses, and lightweight concrete grades were tested. An artificial neural network was used to predict the ultimate load capacity and axial shortening based on the experimental results. The neural network predictions were found to be in acceptable agreement with the experimental results based on linear regression analysis.
Experimental investigation on circular hollow steel columns in filled with li...eSAT Journals
Abstract
Composite Circular hollow Steel tubes with and without GFRP infill for three different grades of Light weight concrete are tested for
ultimate load capacity and axial shortening , under Cyclic loading. Steel tubes are compared for different lengths, cross sections and
thickness. Specimens were tested separately after adopting Taguchi’s L9 (Latin Squares) Orthogonal array in order to save the initial
experimental cost on number of specimens and experimental duration. Analysis was carried out using ANN (Artificial Neural
Network) technique with the assistance of Mini Tab- a statistical soft tool. Comparison for predicted, experimental & ANN output is
obtained from linear regression plots. From this research study, it can be concluded that *Cross sectional area of steel tube has most
significant effect on ultimate load carrying capacity, *as length of steel tube increased- load carrying capacity decreased & *ANN
modeling predicted acceptable results. Thus ANN tool can be utilized for predicting ultimate load carrying capacity for composite
columns.
Keywords: Light weight concrete, GFRP, Artificial Neural Network, Linear Regression, Back propagation, orthogonal
Array, Latin Squares
Robots play important roles in day to day
activities of human endeavour and can perform
complex tasks speedily and accurately. Robots are
employed to imitate human behaviours and then
apply these behaviours to the skills that lead to
achieving a certain task in solving the challenges
faced by impaired people in society. This robotic arm
was achieved using light-weight steel iron for the
frames, a moderate torque MG995 Towerpro, and
servo motor. Two Atmega328 Arduino
microcontroller was employed to control the motors
through the use of pulse width modulation
technique. Mathematical models were developed for
the mechanism to represent the kinematics involved
at each joint with mathematical variables. Then, the
stability of the system was carried out using a step
input signal being a type zero system.
Availability analysis of parallel transit fuel system in petrol engine under ...eSAT Publishing House
This document summarizes a research paper that analyzes the availability of a parallel transit fuel system in a petrol engine. The fuel system has two subsystems (A and B) in series, with subsystem A having two fuel sources as a backup. Subsystem failures follow an exponential distribution and repairs follow a general distribution. The author uses Laplace transforms to obtain equations governing the behavior of the system and its state probabilities. Key results include expressions for the steady-state probabilities of different system states and the long-term availability of the overall fuel system.
This document discusses vibration suppression of a vehicle-bridge interaction system using multiple tuned mass dampers (TMDs). It presents a mathematical model of a system consisting of a vehicle, bridge beam, and three TMDs placed at different locations on the bridge. The model approximates the bridge deflection using the first four mode shapes. Equations of motion are derived for the vehicle, TMDs, and bridge using Lagrange's equations. It is found that placing TMDs at the anti-nodes of the first and second mode shapes is most effective for vibration suppression.
Investigation of behaviour of 3 degrees of freedom systems for transient loadseSAT Journals
Abstract
In this work, the energies dissipated by the spring mass damper system with three degrees of freedom are modelled and simulated for three types of external loads, namely, constant load, exponential decaying load overtime and a partial load over a time period. Two models of the spring mass damper system are modelled and the governing equations are derived. The velocities of the oscillators are estimated by solving the corresponding governing equations for loss of factor of 0.15. The kinetic and potential energies are calculated using the mass, velocity and stiffness of the oscillators and total energy is estimated. , when the load is changed from full load to a partial load over a time period, there is significant increase in the displacement and the velocity at near 0.75 sec, which means it dissipates more energy The contribution of the kinetic energy is minimal for oscillator 2 in all cases and the total energy is constituted mostly of potential energy and there is a substantial contribution both by kinetic and potential energy of oscillator 1 and 3 is presented in this paper. Index Terms: Vibration, 3 Degrees of freedom, Dampers, Loss factor, Transient loads.
A parametric study of x and v bracing industrial steel structureeSAT Journals
Abstract Severe earthquakes have an extremely low probability of occurrence during a structures life. If the earthquakes to be resisted by the structure elastically, it would require an expensive lateral load resisting system, which is not warranty. The structure may lose its aesthetic and functionality due to minor tremors and needs repairs; it will be a very unfavourable design. In addition to earthquake forces there may be wind or any vibrations which induce lateral loads in a structure. In our work we have taken only the earthquake load to find a system which balances the lateral loads and minimizes the displacements of the floors. With the literature review, it was founded that bracing in a structural system reduces the story drift and reduces the lateral force effect. To examine the performance of the bracings, bracing types like X and V bracings are considered and an analysis is performed in ETABS software. The results are studied, discussed and concluded for the best bracing system among both in our project. Keywords: Bracings, Time – History method
Seismic analysis of high damping rubber bearings for base isolationeSAT Journals
This document analyzes the seismic behavior of high damping rubber bearings used for base isolation of structures. It describes modeling a rubber bearing in ANSYS and performing a transient analysis using the displacement time history from the 1940 El Centro earthquake. The analysis found that the bearing could withstand displacements up to 350% of the rubber layer thickness without cavitation occurring in the rubber. Stresses induced in the bearing remained below permissible limits, indicating it could effectively isolate structures from ground motions up to 0.3g accelerations.
A software framework for dynamic modeling of dc motors at robot jointseSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Stress analysis on steering knuckle of the automobile steering systemeSAT Journals
Abstract Steering Knuckle plays major role in many direction control of the vehicle it is also linked with other linkages and supports the vertical weight of the car. Therefore, it requires high precision, quality, and durability. The main objective of this work is to explore performance opportunities, in the design and production of a steering knuckle. This can be achieved by performing a detailed load analysis. Therefore, this study has been dealt with two steps. First part of the study involves modeling of the steering knuckle with the design parameters using the latest modeling software, and also it includes the determination of loads acting on the steering knuckle as a function of time. This is done for finding out the minimum stress area. Then the stress analysis was performed using analysis software. The steering knuckle can be modeled, and analyzed under the actual load conditions. This may also improve the depth knowledge of its function and performance in terms of durability and quality. Keywords: Steering knuckle, stress analysis and Finite Element Analysis (FEA).
Stress analysis on steering knuckle of the automobile steering systemeSAT Publishing House
The document summarizes stress analysis performed on an automobile steering knuckle. It first describes the modeling of the steering knuckle using CAD software and applying loads equivalent to real-world conditions. A finite element analysis is then carried out to determine stress distributions and areas of high stress. The results show maximum stress concentrations that need to be considered in the steering knuckle design to avoid frequent failures and improve reliability.
Comparative Analysis of Multiple Controllers for Semi-Active Suspension SystemPrashantkumar R
International Conference on Emerging Research in Computing, Information, Communication and Applications, ERCICA 2014, held on 01-02 Aug 2014 in Nitte Meenakhsi Institute of Technology, Bangalore, India
Paper ID: 600
Similar to Comparative study of a flexible and rigid two degree of (20)
Hudhud cyclone caused extensive damage in Visakhapatnam, India in October 2014, especially to tree cover. This will likely impact the local environment in several ways: increased air pollution as trees absorb less; higher temperatures without tree canopy; increased erosion and landslides. It also created large amounts of waste from destroyed trees. Proper management of solid waste is needed to prevent disease spread. Suggested measures include restoring damaged plants, building fountains to reduce heat, mandating light-colored buildings, improving waste management, and educating public on health risks. Overall, changes are needed to water, land, and waste practices to rebuild the environment after the cyclone removed green cover.
Impact of flood disaster in a drought prone area – case study of alampur vill...eSAT Publishing House
1) In September-October 2009, unprecedented heavy rainfall and dam releases caused widespread flooding in Alampur village in Mahabub Nagar district, a historically drought-prone area.
2) The flood damaged or destroyed homes, buildings, infrastructure, crops, and documents. It displaced many residents and cut off the village.
3) The socioeconomic conditions and mud-based construction of homes in the village exacerbated the flood's impacts, making damage more severe and recovery more difficult.
The document summarizes the Hudhud cyclone that struck Visakhapatnam, India in October 2014. It describes the cyclone's formation, rapid intensification to winds of 175 km/h, and landfall near Visakhapatnam. The cyclone caused extensive damage estimated at over $1 billion and at least 109 deaths in India and Nepal. Infrastructure like buildings, bridges, and power lines were destroyed. Crops and fishing boats were also damaged. The document then discusses coping strategies and improvements needed to disaster management plans to better prepare for future cyclones.
Groundwater investigation using geophysical methods a case study of pydibhim...eSAT Publishing House
This document summarizes the results of a geophysical investigation using vertical electrical sounding (VES) methods at 13 locations around an industrial area in India. The VES data was interpreted to generate geo-electric sections and pseudo-sections showing subsurface resistivity variations. Three main layers were typically identified - a high resistivity topsoil, a weathered middle layer, and a basement rock. Pseudo-sections revealed relatively more weathered areas in the northwest and southwest. Resistivity sections helped identify zones of possible high groundwater potential based on low resistivity anomalies sandwiched between more resistive layers. The study concluded the electrical resistivity method was useful for understanding subsurface geology and identifying areas prospective for groundwater exploration.
Flood related disasters concerned to urban flooding in bangalore, indiaeSAT Publishing House
1. The document discusses urban flooding in Bangalore, India. It describes how factors like heavy rainfall, population growth, and improper land use have contributed to increased flooding in the city.
2. Flooding events in 2013 are analyzed in detail. A November rainfall caused runoff six times higher than the drainage capacity, inundating low-lying residential areas.
3. Impacts of urban flooding include disrupted daily life, damaged infrastructure, and decreased economic activity in affected areas. The document calls for improved flood management strategies to better mitigate urban flooding risks in Bangalore.
Enhancing post disaster recovery by optimal infrastructure capacity buildingeSAT Publishing House
This document discusses enhancing post-disaster recovery through optimal infrastructure capacity building. It presents a model to minimize the cost of meeting demand using auxiliary capacities when disaster damages infrastructure. The model uses genetic algorithms to select optimal capacity combinations. The document reviews how infrastructure provides vital services supporting recovery activities and discusses classifying infrastructure into six types. When disaster reduces infrastructure services, a gap forms between community demands and available support, hindering recovery. The proposed research aims to identify this gap and optimize capacity selection to fill it cost-effectively.
Effect of lintel and lintel band on the global performance of reinforced conc...eSAT Publishing House
This document analyzes the effect of lintels and lintel bands on the seismic performance of reinforced concrete masonry infilled frames through non-linear static pushover analysis. Four frame models are considered: a frame with a full masonry infill wall; a frame with a central opening but no lintel/band; a frame with a lintel above the opening; and a frame with a lintel band above the opening. The results show that the full infill wall model has 27% higher stiffness and 32% higher strength than the model with just an opening. Models with lintels or lintel bands have slightly higher strength and stiffness than the model with just an opening. The document concludes lintels and lintel
Wind damage to trees in the gitam university campus at visakhapatnam by cyclo...eSAT Publishing House
1) A cyclone with wind speeds of 175-200 kph caused massive damage to the green cover of Gitam University campus in Visakhapatnam, India. Thousands of trees were uprooted or damaged.
2) A study assessed different types of damage to trees from the cyclone, including defoliation, salt spray damage, damage to stems/branches, and uprooting. Certain tree species were more vulnerable than others.
3) The results of the study can help in selecting more wind-resistant tree species for future planting and reducing damage from future storms.
Wind damage to buildings, infrastrucuture and landscape elements along the be...eSAT Publishing House
1) A visual study was conducted to assess wind damage from Cyclone Hudhud along the 27km Visakha-Bheemli Beach road in Visakhapatnam, India.
2) Residential and commercial buildings suffered extensive roof damage, while glass facades on hotels and restaurants were shattered. Infrastructure like electricity poles and bus shelters were destroyed.
3) Landscape elements faced damage, including collapsed trees that damaged pavements, and debris in parks. The cyclone wiped out over half the city's green cover and caused beach erosion around protected areas.
1) The document reviews factors that influence the shear strength of reinforced concrete deep beams, including compressive strength of concrete, percentage of tension reinforcement, vertical and horizontal web reinforcement, aggregate interlock, shear span-to-depth ratio, loading distribution, side cover, and beam depth.
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Comparative study of a flexible and rigid two degree of
1. IJRET: International Journal of Research in Engineering and Technology e-ISSN: 2319-1163 p-ISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 10 | Oct-2013, Available @ http://www.ijret.org 11
COMPARATIVE STUDY OF A FLEXIBLE AND RIGID TWO DEGREE OF
FREEDOM HALF CAR MODEL
Saurav Talukdar1
, Anupam Mazumdar2
, Karuna Kalita3
1
Mechanical Engineering Department, Indian Institute of Technology Bombay, Powai, Mumbai – 400076, India
2
Civil Engineering Department, Indian Institute of Technology Guwahati, Guwahati – 781039, India
3
Mechanical Engineering Department, Indian Institute of Technology Guwahati, – 781039, karuna.kalita@iitg.ernet.in
Abstract
Ride quality is concerned with the feel of the passenger in the environment of a moving vehicle. It is one of the key indices in
determining comfort levels of a vehicle. Although, “ride comfort” evaluation is subjective in nature, researchers have developed
mathematical models to study and evaluate vehicle ride performance. Some popular models for vehicle ride analysis are – quarter car
model, two dof (degree of freedom) and four dof half car model. These models model the chassis as a rigid body. This work removes
this assumption and models the chassis of the vehicle as a flexible beam on a spring damper system at the front and rear using Euler
beam theory. This elastic model has two dof – vehicle bounce and pitch, and has been compared with the rigid two dof model. Euler
beam theory and Lagrangian mechanics are used to derive the equations of motion. Finite element method is used to validate this
model. Experimental validation of the natural frequencies of this flexible beam is presented.
Keywords: Flexible ride model, Elastic ride model
---------------------------------------------------------------------***-------------------------------------------------------------------------
INTRODUCTION
Research in the area of vehicle dynamics has progressively
become more systematic and intensive since the early sixties.
Mathematical modeling has become an important step to
understand the underlying dynamics of the system. The
development of computers has provided the computational
power to have high fidelity models of real systems. Multibody
dynamics (MBS) [1], Finite Element Method (FEM) [2] etc.
are widely used in mechanical design and analysis.
Vehicle ride quality is considered to be one of the most
important parameters to evaluate the performance of a vehicle.
The designer has to achieve good ride comfort for the driver
and passengers with acceptable control of body attitude and
adequate control of dynamic tyre loads within the constraint of
having a restricted amount of suspension working space
available. These issues are classified as ‘primary ride’ and are
studied with the help of mathematical models [3]. Some of the
most popular and simple models are- quarter car model [4],
two dof half car model [4], four dof half car model [5] and
seven dof ride model [3]. These models consider the sprung
masses and unsprung masses as rigid bodies. However, in
reality the chassis is flexible and its flexibility needs to be
considered to completely understand the dynamics. Vehicle
ride models which have incorporated the flexible chassis are
based on flexible multibody dynamics [6]. Finite element
method is used to model the sprung mass as a flexible beam or
as a flexible plate [7]. Some models use model reduction
techniques to reduce the order of these models [8]. These
models [6, 7, 8] are based on numerical simulation and do not
have a close form solution.
This paper presents an analytical model considering the
sprung mass as a flexible beam on a spring damper system at
the front and rear. A flexible beam system has infinite degrees
of freedom. However, the variables of interest in this context
are - the overall translation and rotation of the beam. Hence,
this model also has two degrees of freedom – bounce and pitch
like the conventional two dof half car model [4], which is the
rigid body counterpart. Euler beam theory [9] is used to model
the beam and Lagrangian mechanics [10] along with the
concept of tracking frame [11] is used to derive the equations
of motion. The conventional two dof model will be referred to
as 'rigid two dof model' and model developed in this paper
will be referred to as 'flexible two dof model’. The results are
validated by finite element and experimental results. A
comparison between both the models in time domain and
frequency domain is presented and the differences are
discussed. The paper is organized as follows: Section 1
contains the vehicle models. Finite element modeling of a
flexible beam is explained in Section 2. Section 3 presents the
results and discussion, followed by summary in Section 4.
VEHICLE MODELS
The two vehicle models compared in this paper viz. the rigid
two dof model and the flexible two dof model, which are
presented below.
2. IJRET: International Journal of Research in Engineering and Technology e-ISSN: 2319-1163 p-ISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 10 | Oct-2013, Available @ http://www.ijret.org 12
RIGID TWO DOF MODEL
A schematic of the rigid two dof model is shown in Figure 1.
This model does not consider the sprung mass and unsprung
mass to be distinct. It has one combined mass (ms) which
represents half of a vehicle supported on front (k1 and c1 are
the front suspension stiffness and damping respectively) and
rear suspension (k2 and c2 are the rear suspension stiffness and
damping respectively). The springs and dampers are
considered to be at the extreme ends. The two degrees of
freedom are - vertical displacement of the chassis (xs) and the
pitching motion (φ). The distance of the centre of gravity (CG)
from the front (l1) and rear axle (l2) are used to write the
displacements of the front and rear end as well as moment arm
for the moment equation (J is the moment of inertia). The
inputs to this model are the road excitations at the front (xrf)
and rear (xrr). The main assumptions of this model are-
a) Unsprung mass is not considered.
b) Sprung mass is considered to be a rigid body.
c) The linear suspension spring and viscous damping is
assumed.
d) Springs and dampers are considered to be at the ends.
e) Small pitch displacement.
The equations of motion are –
1 1 2 2+ + = +Mx Cx Kx F u F u&& & (1)
where,
0
0
sm
J
=
M , 1 2 2 2 1 1
2 2
2 2 1 1 1 1 2 2
c c c l c l
c l c l c l c l
+ −
= − +
C , 1 2 2 2 1 1
2 2
2 2 1 1 1 1 2 2
k k k l k l
k l k l k l k l
+ −
= − +
K
1 2
1
1 1 2 2
c c
c l c l
= −
F , 1 2
2
1 1 2 2
k k
k l k l
= −
F , 1
rf
rr
x
x
=
u
&
&
, 2
rf
rr
x
x
=
u ,
sx
ϕ
=
x
Figure1. Rigid two dof half car model
FLEXIBLE TWO DOF MODEL
A schematic of the flexible two dof model is shown in Figure
2. This model considers the sprung mass as an Euler beam
supported on a spring damper system at the front and rear end
of the beam. The main assumptions of this model are –
a) Unsprung mass is not considered.
b) The beam is considered to undergo planar motion and
there is only in-plane bending.
c) The beam is made of homogeneous material.
d) Linear suspension spring and viscous damping is
assumed.
e) Small pitch displacement.
f) The extension of the spring due to the different
vibration modes has been neglected. The expression
for potential energy of the spring is written
considering the rigid body mode of vibration only.
In Figure 2, the coordinate system n is an inertial reference
frame whereas the coordinate system b is a body fixed frame
system.
3. IJRET: International Journal of Research in Engineering and Technology e-ISSN: 2319-1163 p-ISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 10 | Oct-2013, Available @ http://www.ijret.org 13
Figure 2. Flexible two dof half car model
Position vector (R) of any point P can be written as
2 1 2
ˆ ˆˆ( , , ) ( ) ( , ) ( ) ( , )x y t y x t y t n xb v x t b= + = + +0R R r (2)
The velocity of point P with respect to the inertial frame can be written as
( ) ( ) ( ){ }
( ) ( ) ( )
2 2 3 1 2
2 2 1
ˆ ˆ ˆ ˆˆ
ˆ ˆˆ
x,y,t y t n b b xb v x,t b
x,y,t y t n x b b
ν θ
ν θ θν
= + + × +
= + + −
R
R
&& &&
& && &&
The unit vector in the inertial frame is related to the body fixed frame by
1 1
2 2
33
ˆ ˆcos sin 0
ˆ ˆsin cos 0
ˆ ˆ0 0 1
bθ θ n
θ θ b n
nb
−
=
Using small angle approximation sin ,cos 1θ θ θ≈ ≈ and neglecting the nonlinear terms the velocity of point P in the body frame is
given by equation (3).
2
ˆ( )y v x bθ= + +R && & & (3)
The kinetic energy of the beam (T) can be expressed as
2 2 2 2
2 2 2
0
1
( 2 2 2 )
2
1 1 1
2 2 2
L
L L L
T ρA y x x y y x
my J ρA dx ρA xdx ρAy dx myL
ν θ θν ν θ
θ ν θ ν ν θ
= + + + + +
= + + + + +
∫
∫ ∫ ∫
& & && & && & &
& & && & && & &
(4)
where m is the mass of the beam and
2
0
1
J mL
3
= is the moment of inertia of the beam. Here y and θ are the function of time
only whereas v is a function of both position and time. The potential energy of the beam (U) with the spring and damper system is
formulated. The potential energy of the system has contributions from both the springs and strain energy of the beam. The potential
energy of the system is given by -
4. IJRET: International Journal of Research in Engineering and Technology e-ISSN: 2319-1163 p-ISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 10 | Oct-2013, Available @ http://www.ijret.org 14
( ) { }
2 2
1 1 1 2 2 2
1 1
2 2 L
U k y x θ - y k y (L - x )θ y EI dxν′′= + + + − + ∫ (5)
According to the Extended Hamiltonian principal [10],
where, L is the Lagrangian and Wnc is the non-conservative work [10] and L T U= − . The Rayleigh term, R is given by [10] as
( )
2
2
1 1 1 2 2 2
1 1
( )
2 2
R c (y x y ) c y L x - yθ θ= + − + + −& && & & & (6)
Using Lagrange’s equation,
0
d T T U R
dt q q q q
∂ ∂ ∂ ∂
− + + =
∂ ∂ ∂ ∂ & &
(7)
where, q is the generalized coordinate. The generalised coordinates for this system are - , ,y vθ . Using these generalised coordinates
and equation (7), the governing dynamical equations of the system under consideration is given by equation (8) to (10).
( )
( ) ( ) ( )
1 1
2 2 1 1 2 2
1 1 2 2 1 1 2 2
1
2
( ) ( )
L
my ρA dx mL k y x
k y L x c y x c y L x
k y k y c y c y
ν θ θ
θ θ θ
+ + + +
+ + − + + + + −
= + + +
∫ &&&&&&
& && &
& &
(8)
( ) ( ) ( )
( )
2 2
0 1 1 1 2 2 2 2 2 2
1 1 1 1 1 1 2 2 2 2 2 2
1
2L
J ρA xdx mLy k x y x θ k L - x y k L - x θ c Ly c L
k x y c x y k L - x y c (L - x )y
θ ν θ
+ + + + + + + + =
+ + +
∫&& &&& && &
& &
(9)
(10)
1 2 1 2, andk ,k c , c are the stiffness and damping coefficients of front and rear springs and dampers respectively. The consequence of
assumption (f) of this model is that it gives accurate results for 1 20and 0x x= = . Hence, the spring and damper system has to be
attached at the ends. However, 1 2andx x have been retained in the derivation even if they are taken to be zero in the simulations so as
to explain the derivation for a general location of springs. If 1 20 & 0x x≠ ≠ , the problem can be formulated again with slight
modification of the potential energy expression (equation (5)) and Rayleigh term (equation (6)). The modified potential energy
expression for general spring-damper location is -
( ) { }
2 2
1 1 1 2 2 2
1 1
2 2 L
U k y x θ v - y k y (L - x )θ v y EI dxν ′′= + + + + + − + ∫ (11)
The modified Rayleigh term is-
( )
2
2
1 1 1 2 2 2
1 1
( )
2 2
R c (y x v y ) c y L x v - yθ θ= + + − + + − +& && & & & & & (12)
Using equation (4), (11), (12) and (7), the new set of governing equations of motion can be obtained. Henceforth, this work would
consider the case of 1 20and 0x x= = .
The natural frequencies and mode shapes are obtained by solving the free vibration problem, hence, the damping and base excitations
are not considered. The damping is neglected as the quantities of interest are the undamped natural frequency and its corresponding
mode shapes. To determine the mode shapes and natural frequencies, let
( ) ( ) ( )expx,t V x j tν ω= (13)
4
4
0
v
ρA ρA(x y) EI
x
ν θ
∂
+ + + =
∂
&&&& &&
0ncLdt W dtδ δ+ =∫ ∫
5. IJRET: International Journal of Research in Engineering and Technology e-ISSN: 2319-1163 p-ISSN: 2321-7308
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Volume: 02 Issue: 10 | Oct-2013, Available @ http://www.ijret.org 15
( ) ( )expθ t j tω= Θ (14)
( ) ( )expy t Y j tω= (15)
Using equations (13) to (15) in (8) to (10), neglecting the damping and base excitation along with the substitution,
( ) ( )W x V x x= + Θ
the equations are-
( ) ( ){ }2 2
1 2 1 1 2 2 0
L
k k m Y ρA Wdx k x k L xω ω+ − − + Θ + − =∫ (16)
( ) ( ){ }22 2 2
1 1 2 2 1 1 2 2
1
0
2L
ρA xWdx Y k x k L x mL k x k L xω ω
− + + − − + Θ + − =
∫ (17)
2 2
0ivρA W ρA Y EIWω ω− − + = (18)
Substituting
L
Wdx α=∫ in equation (16),
( ){ }2
1 1 2 2
2
1 2
ρA α k x k L x
Y
k k m
ω
ω
− Θ + −
=
+ −
(19)
Using equation (19) in (18),
( ){ }2
1 1 2 22 2
2
1 2
ρA α k x k L xivEIW ρA W ρA
k k m
ω
ω ω λα ψ
ω
− Θ + −
− = = + Θ + −
(20)
where,
( )
22
2
1 2
A
k k m
ρ ω
λ
ω
=
+ −
and
( )2
1 1 2 2
2
1 2
( )A k x k L x
k k m
ρ ω
ψ
ω
+ −
=
+ −
.
The general solution of equation (20) can be written as,
( ) 1 2 3 4cos sin cosh sinhW x a kx a kx a kx a kx Bα Dθ= + + + − + (21)
where,
( )2
1 1 2 24
2 2
1 2 1 2
, ,
+ −
= = =
+ − + −
k x k L xρA ρA
k B D
EI k k m k k m
ω
ω
ω ω
Substituting the following expression in equation (17) and using equation (19),
( )
L
xW x dx β=∫
( )
( )
2 2
1 1 2 2
1 2
22 2
1 1 2 2 1 1 2 2
1
2
1
( )
2
ρA β k x k L x mL Bα
m β m α
k x k L x D k x k L x mL
ω ω
ω
− + − −
Θ= = −
+ − − + − −
(22)
where,
( )
( )
( )
2
1
22 2
1 1 2 2 1 1 2 2
2
1 1 2 2
2
22 2
1 1 2 2 1 1 2 2
1
( )
2
1
2
1
( )
2
A
m
k x k L x D k x k L x mL
k x k L x mL B
m
k x k L x D k x k L x mL
ρ ω
ω
ω
ω
=
+ − − + − −
+ − −
=
+ − − + − −
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The boundary conditions used to solve this problem are
1. The choice of the body fixed frame b gives (0) 0W = and ( )W L L= Θ
2. The bending moment at both the ends is zero, which implies
2
2
(0)
0
d W
dx
= and
2
2
( )
0
d W L
dx
=
Using these four conditions and substituting equation (21) in the definitions of α and β, a system of six homogenous equations
with 1 2 3 4[ ]T
a a a a α β=x as unknowns can be obtained as
=Dx 0 (23)
where, Dis a 6 6× matrix described below. The detailed steps are
Using ( )0 0W = in equation (21),
( )1 3 2 1 0a a B Dm α Dm β+ − + + = (24)
Using ( )W L L= Θ in equation (21),
( ){ } ( )1 2 3 4 2 1cos sin cosh sinh 0a kL a kL a kL a kL B D L m α D L m β+ + + − + − + − = (25)
Using ( )0 0EIW′′ = in equation (21),
1 3 0a a− = (26)
Using ( ) 0EIW L′′ = in equation (21),
1 2 3 4cos sin cosh sinh 0a kL a kL a kL a kL− − + + = (27)
Using equation (21) in definition of α,
( ) ( ) ( )1 2 3 4sin cos 1 sinh cosh 1 1 0a kL a kL a kL a kL k BL α kDLθ− − + + − − + + =
( ) ( ) ( )1 2 3 4 2 1or, sin cos 1 sinh cosh 1 1 0a kL a kL a kL a kL k BL m DL α m kDLβ− − + + − − + + + = (28)
Using equation (21) in definition of β,
( ) ( )
( ) ( )
1 2
3 4
2 2 2 2 2
sin cos 1 sin cos
sinh cosh 1 cosh sinh
1 1
0
2 2
a kL kL kL a kL kL kL
a kL kL kL a kL kL kL
Bk L α k β Dk L θ
+ − + − +
− + + − −
− + =
( ) ( )
( ) ( )
( )
1 2
3 4
2 2 2 2 2 2 2
2 1
, sin cos 1 sin cos
sinh cosh 1 cosh sinh
1 1
0
2 2
or a kL kL kL a kL kL kL
a kL kL kL a kL kL kL
Bk L Dk L m α Dk L m k β
+ − + − +
− + + − −
+ + − =
(29)
Equations (24) to (29) can be written in the form of equation (23) where,
( )
( ){ } ( )
( )
2
2 1
2 1
1 0 1 0
1
cos sin cosh sinh
1 0 1 0 0 0
cos sin cosh sinh 0 0
sin 1 cos sinh cosh 1 1
sin sin sinh cosh
cos 1 cos cosh 1 sin
B Dm Dm
kL kL kL kL B D L m D L m
kL kL kL kL
kL kL kL kL k BL m DL m KDL
kL kL kL kL kL kL kL
kL kL kL kL
− +
− + − −
−
= − −
− − − + +
− −
+ − + −
D
2 2 2 2
2 1
2
h 2 2
k L k L Dm
(B Dm ) k
kL
− + − +
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[ ]1 2 3 4
T
a a a a α β=x
To ensure non trivial solutions the determinant of the coefficient matrix D has to be zero. This gives the values of k corresponding to
the natural angular frequencies of the system. Using these values of k and assuming 1 1a = , the other unknowns in x can be obtained,
which can then be used to compute the mode shapes using equation (30).
( ) ( )V x W x x= − Θ (30)
(W(x) in equation (30) could be be obtained from equation (21))
The obtained mode shape V(x) will be used to solve the forced vibration problem i.e., the system with spring, damper and base
excitation. Using separation of variables the displacement of the beam as a function of space and time in the body fixed coordinate
system is given by equation (31).
( , ) ( ) ( )v x t V x tη= (31)
Substituting equation (31) in equation (8) and (9),
( ) ( ){ }
( ) ( ){ }
1 1 2 2
1 1 2 2 1 1 2 2 1 1 2 2
1
( )
2L
my ρA V x dx mL k y x k y L- x
c y x c y L- x k y k y c y c y
η θ θ θ
θ θ
+ + + + + + +
+ + + = + + +
∫ &&&&&&
& && & & &
(32)
( )
( ) ( )
( )
0 1 1 1
2 2
2 2 2 2 2 2
1 1 1 1 1 1 2 2 2 2 2 2
1
( )
2
( )
L
J ρA V x xdx mLy k x y x θ
k L - x y k L - x θ c Ly c L
k x y c x y k L - x y c L - x y
θ η
θ
+ + + + +
+ + + =
+ + +
∫&& && &&
&&
& &
(33)
Using equation (31) in (10), multiplying both sides by W(x) and integrating between 0 to L,
4
4
( ) ( ) ( )
( )
( ) ( ) 0
L L
L L
ρA V x W x dx ρA xW x dx
d V x
ρAy W x dx EI W x dx
dx
η θ
η
+ +
+ =
∫ ∫
∫ ∫
&&&&
&&
(34)
The equations (32) to(34) can be re-written in the standard form as in equation (1).
1 1 2 2+ + = +Mx Cx Kx F u F u&& &
where,
1 1
1 2
2 2
, ,
y
y y
y y
θ
η
= = =
x u u
&
&
0
0.5 ( )
0.5 ( )
( ) ( ) ( ) ( )
L
L
L L L
m mL A V x dx
mL J A xV x dx
A W x dx A xW x dx A V x W x dx
ρ
ρ
ρ ρ ρ
=
∫
∫
∫ ∫ ∫
M
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1 2 1 1 2 2
2
2 2
1 2 1 1 2 2
2 2
1 1 2 2 1 1 2 2
4
4
1 2 1 2
1 1 1 2 2 2 1 1 2 2
( ) 0
0
0 0 0
( ) 0
( ) 0
( )
0 0 ( )
( ) , ( )
0 0 0 0
L
c c c x c L x
c L c L
k k k x k L x
k x k x k x k L x
d V x
EI W x dx
dx
c c k k
c x c L x k x k L x
+ + −
=
+ + −
= − + −
= − = −
∫
C
K
F F
Each mode shape obtained from equation (30) can be used in equation (32) to (34) along with numerical integration techniques to
obtain the corresponding time response function ( )i tη , bounce displacement of CG ( ( ) ( ))
2
i i
L
y t tθ+ and pitch displacement of CG
( )i tθ .The general response of the beam in the body fixed coordinate system is given by
0
( , ) ( ) ( )i i
i
v x t V x tη
∞
=
= ∑ (35)
where, ( )iV x is the mode shape corresponding to the ith
natural frequency and ( )i tη is the time response of the beam corresponding
to the ith
mode. The net bounce displacement and pitch displacement of the CG is the summation due to each mode and can be
computed using equation (36) and (37).
1
( ) ( ( ) ( ))
2
i i
i
L
y t y t tθ
∞
=
= +∑ (36)
1
( ) ( )i
i
t tθ θ
∞
=
= ∑ (37)
Equations (35) to (37) along with (32) to (34) and initial conditions provide a solution to the forced excitation problem.
FINITE ELEMENT MODELING
Finite element method has been used to calculate the natural frequency and its associated modes of the flexible beam supported by two
springs at the both ends. The damping is not considered for finite element analysis. The elemental equations of stiffness and mass
matrices have been derived for bending motion of the beam assuming Euler-Bernoulli bending theory [13]. Figure 3 shows slender
beam supported by two springs at both ends. The beam is discretized with (N-1) two noded elements generating N nodes. Figure 4
shows any arbitrary element with the two degrees of freedom per node. In Figure 4, iv and 1iv + represents the displacements of ith
and
(i+1)th
node respectively and iϕ and 1iϕ + represents the deflections of ith
and (i+1)th
node respectively.
Figure 3. Finite element model
1k 2k
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Figure 4. One finite element
The elemental stiffness and mass matrices are shown in equations (38) and (39) respectively.
2 2
2 2
156 22 54 13
22 4 13 3
54 13 156 22420
13 3 22 4
e
l l
l l l lAl
l l
l l l l
ρ
−
− −
=
− −
− − −
M (38)
where ρ is the density, A is the cross sectional area and the l is the length of the finite element.
2 2
3
2 2
12 6 12 6
6 4 6 2
12 6 12 6
6 2 6 4
e
l l
l l l lEI
l ll
l l l l
−
−
=
− − −
−
K (39)
where E is the Young’s modulus, I is the flexural moment of inertia and the l is the length of the finite element.
The elemental spring and mass matrices of each element are derived and assembled to give the complete equation of motion. The
complete equation of motion can be written as
G G G Gq q+ =M K 0&& (40)
where GM is the global mass matrix whose size is ( )2 2N N× , GK is the global stiffness matrix whose size is ( )2 2N N× and
Gq is the nodal displacements whose size is ( )2 1N × . The boundary conditions have been applied by incorporating the spring
stiffness at the 1st
and Nth
nodes. The eigenvalue and eigenvectors are calculated using the 'eig' command of MATLAB®
as follows:
[ ] ( ), ,G Geval evec eig= K M (41)
where eval gives the squares of the natural frequencies and evac gives the corresponding mode shapes.
RESULTS AND DISCUSSION
A comparison between the rigid and the flexible models
described in the previous sections is presented here. The
numerical parameters used for the simulation are tabulated
(see Table 3 and Table 4) in the appendix. A MATLAB code
has been written to calculate the natural frequencies and the
mode shapes for the flexible two dof model. The natural
frequencies and mode shapes obtained from the analytical
solutions are validated using finite element analysis. The beam
is modeled as an Euler-Bernoulli beam. A total number of 100
elements are considered with two degrees of freedom per
node. The first four modes of the flexible two dof model are
used to calculate the time response of the beam. The first four
natural frequencies obtained from the analytical solution of
flexible two dof model and FEM model is tabulated in Table
1.
Table 1. Natural frequencies (in Hz) of the flexible two dof
model from analytical and FEM approach.
Model ω1 ω2 ω3 ω4
Analytical 10.4837 18.2553 243.8926 670.1111
FEM 10.4861 18.2404 243.8914 670.1108
A small scale experimental setup has been built to verify the
natural frequencies obtained from the analytical model. The
setup consists of a mild steel beam on two springs of equal
iv 1iv +
iϕ 1iϕ +
i 1i +
l
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stiffness at the ends. The parameters of this setup are listed in
the appendix (see Table 5). The beam is excited with an
impulse hammer and two accelerometers are mounted at two
points on the beam to capture the response. The impulse
hammer and accelerometers are connected to a Data
Acquisition System. A picture of the experimental setup is
shown in Figure 3. The first four natural angular frequencies
of this beam obtained from the analytical model, FEM and
experiment are listed in Table 2.
Table 2. Natural angular frequencies (in rad/s) of the
experimental beam from analytical model, FEM model and
experiment
Model ω1 ω2 ω3 ω4
Analytical 66.892 185.537 311.019 549.781
FEM 66.892 185.538 311.018 549.783
Experiment 69.12 182.20 314.11 552.34
Figure 3. Experimental setup to verify natural frequencies
Figure 4 shows the acceleration frequency response function
(FRF) obtained from the experimental setup. Peaks can be
observed in this experimentally obtained FRF for frequencies
close to the natural frequencies predicted by the analytical
model. This is supportive of the analytical solution described
in the previous section. However, peaks are also seen for
frequencies which are not the natural frequencies e.g., 150
rad/s, 402 rad/s etc. These could be due to the unaccounted
structural damping of the system, the cylindrical rods welded
at the end part of the beam to hold the springs, non-uniformity
of beam etc.
The mode shapes of the beam have been obtained using the
analytical model and finite element method. Figure 5 shows
the shape function i.e., W(x), computed using the analytical
method (see Figure 5 (a)) and finite element method (see
Figure 5 (b)). The shape functions (W(x)) were chosen instead
of the vibration mode shapes (V(x)) because it has effect of
both the vibration mode shapes (V(x)) and the pitching motion
( Θ ), and hence it gives a better visualization of the physical
scenario of a beam is undergoing transverse vibration as well
as pitching motion. it is clear Figure 5 that the shape functions
obtained using the analytical model and finite element method
are identical. Thus, Figure5 along with Table 1validate the
analytical method derived in the previous section.
Figure 4. Experimentally obtained FRF of bounce
acceleration.
(a)
(b)
Figure 5. Shape-function (W(x)) along the length of the beam
obtained using analytical method (a) and FEM (b).
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The impulse response function of a dynamic system can be
used to compute the response of the dynamic system to any
arbitrary excitation using the Duhamel’s Integral [12]. Hence,
to understand and compare the dynamic response of the
models, it is important to analyze the unit impulse response of
both the models. The simulation is run for 5 seconds and the
first four modes of the flexible two dof model have been
considered to compute the time response. Figure 6 shows the
bounce displacement (in m) and pitch displacement (in radian)
for unit impulse excitation. It is clear from Figure 6 (a) that the
rigid two dof model under predicts the bounce displacement
(by more than 50%) and has a lower settling time as compared
to the flexible two dof model (~ 30%). Referring to Figure 6
(b), the rigid two dof model over predicts the pitch
displacement (~ 50%) and has a higher settling time as
compared to the flexible two dof model (~ 50%). The pitch
response of the rigid two dof model is sluggish as compared to
that of the flexible two dof model.
(a)
(b)
Figure 6. Bounce displacement (a) and pitch (b) response of
the rigid two dof model and flexible two dof model to unit
impulse.
It is a common practice in vehicle ride dynamics to study the
response of the mathematical models to sinusoidal excitation.
Road surface excitation is irregular/random, but it can be
expressed as combination of sines and cosines with the help of
Fourier Transform. Hence, it is essential to study the response
of these models to sinusoidal base excitation. The front end is
excited by a sinusoid of amplitude 0.01 m and angular
frequency
4
π
rad/second. The rear end is excited by the same
sinusoid but with a phase lag which can be computed using the
length of the vehicle and velocity. The velocity is taken to be 1
m/s and simulation is run for 30 seconds and the first 4 modes
of the flexible two dof model have been considered.
It can be seen from Figure 7 (a) that the rigid two dof model
predicts lower displacement amplitude as compared to the
flexible two dof model. The flexible two dof model
displacement plot (Figure 7 (a)) shows that the transmissibility
is high because the output amplitude (0.04 m) is four times the
input amplitude (0.01 m). Referring to Figure 7 (b), the pitch
amplitude predicted by the rigid two dof model is lower than
the flexible two dof model (~50%).
(a)
(b)
Figure7. Bounce displacement (a) and pitch (b) response of
the rigid two dof model and flexible two dof model to
sinusoidal excitation.
It can be concluded from Figure 6 and Figure 7 that there are
significant differences in the time domain responses of the
rigid two dof model and the flexible two dof model. Figure 8
shows the frequency response function (FRF) of the bounce
displacement. The FRF of the rigid two dof model (Figure 8
(b)) has been computed by using the transfer function. The
same method cannot be used for the flexible two dof model
because of the non-linear M and K matrices. The FRF (Figure
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Volume: 02 Issue: 10 | Oct-2013, Available @ http://www.ijret.org 22
8 (a)) is obtained by solving the time domain system for a
sinusoid of amplitude 1 and some angular frequency. The
amplitude of the response is then calculated and plotted on the
log-log plot corresponding to the angular frequency. 27 points
were used to draw this FRF and these discrete points are then
plotted to obtain an approximate sketch of the bounce
displacement FRF of the flexible two dof model. The points
associated with a box in this plot (see Figure 8(a)) show the
peaks corresponding to the four natural frequencies which are
absent in the FRF of the rigid two dof model (see Figure 8
(b)). The amplitude ratio predicted by the rigid two dof model
is lower than that of the flexible two dof model.
The additional modes of the system are responsible for the
differences in dynamics of both the models. The flexible two
dof model is closer to reality than the rigid two dof model and
significant differences are observed between both the models,
hence, the flexible two dof model should be used to do initial
design calculations and control instead of the rigid two dof
model.
(a)
(b)
Figure 8. Frequency response of bounce of the flexible two
dof model (a) and the rigid two dof model (b).
SUMMARY
A modified two dof model which accounts for the flexibility
of the chassis by modeling it as a flexible beam is presented it
in this paper. Complete set of the resulting dynamics equations
are presented. The impulse response and sinusoidal response
of the models are compared. The rigid two dof model under
predicts the bounce displacement for both the excitation. The
rigid two dof model shows a sluggish pitch response as
compared to the flexible two dof model to unit impulse. The
pitch amplitude predicted by the rigid two dof model is less
than that predicted by the flexible two dof model to sinusoidal
excitation. The settling time of the impulse response of bounce
is lower for the rigid two dof model while for the pitch it is
lower for the flexible two dof model. The bounce
displacement amplitude ratio FRF of the flexible two dof
model exhibits more peaks and higher amplitude ratio. The
flexible two dof model is closer to reality as compared to the
rigid two dof model, and hence should be used for initial
design calculations, simulations and control design. An
extension of the current work would be to develop a four dof
vehicle ride model with sprung mass at the front and rear.
Another work would be to account for tyre flexibility properly
instead of considering it as a linear spring. It is important to
note that only the first four have been used for simulations and
the spring damper system are considered at the ends. The
analytical model has been validated using FEM and
experiments.
REFERENCES
1. Amirouche, Farid., Fundamentals of Multibody
Dynamics, Birkhäuser, Boston, ISBN: 978-0-8176-4236-
5,2006.
2. Krysl, P., A Pragmatic Introduction to the Finite Element
Method for Thermal and Stress Analysis, World Scientific
Publishing Co. Pvt. Ltd., Singapore, ISBN-10: 981-256-
876-X | ISBN-13: 981-270-411-6, 2006.
3. Crolla, D.A., Vehicle Dynamics – Theory into Practice,
Proceedings of the Institution of Mechanical Engineers,
Part D: Journal of Automobile Engineering 210(2): 83-94,
April
1996,doi:10.1243/PIME_PROC_1996_210_250_02.
4. Wong,J.Y., Theory of Ground Vehicles, John Wiley &
Sons, ISBN: 978-0-470-17038-0.
5. Sun, T., Zhang, Y. and Barak, P., 4-DOF Vehicle Ride
Model, SAE Technical Paper 2002-01-1580, presented at
SAE Automotive Dynamics and Stability Conference,
Detroit, USA, May 2002.
6. Goncalves, J.P. and Ambrόsio, J. A., Optimization of
Vehicle suspension Systems for Improved Comfort of
Road Vehicles Using Flexible Multibody Dynamics,
Nonlinear Dynamics 34: 113-131, 2004.
7. Ibrahim, I.M., Crolla, D.A. and Barton, D.C., Effect of
Frame Flexibility on the Ride Vibration of Trucks,
Computers and Structures 58(4): 709-713, February 1996,
doi:10.1016/0045-7949(95)00198-P.
13. IJRET: International Journal of Research in Engineering and Technology e-ISSN: 2319-1163 p-ISSN: 2321-7308
__________________________________________________________________________________________
Volume: 02 Issue: 10 | Oct-2013, Available @ http://www.ijret.org 23
8. Verros, G. andNatsiavas, S., Ride Dynamics of Nonlinear
Vehicle Models Using Component Mode Synthesis,
Journal of Vibration and Acoustics 124(3): 427-434, July
2002,doi:10.1115/1.1473828.
9. Timoshenko, S.P. and Goodier, J.N., Theory of Elasticity,
Tata McGraw-Hill Education Pvt. Ltd., New Delhi,
ISBN-13: 978-0-07-070122-9, 2010.
10. Goldstein, H., Poole, C.P. and Safko, J., Classical
Mechanics, Pearson, ISBN: 978-81-317-5891-5, June
2001.
11. Nayfeh,A. H., Emam,S. A., Preidikman,S., and
Mook,D.T., An Exact Solution for the Natural
Frequencies of Flexible Beams Undergoing Overall
Motions, Journal of Vibration and Control 9(11): 1221-
1229, November 2003, doi: 10.1177/1077546304030692.
12. Meirovitch, L., Analytical Methods in Vibration, Prentice
Hall, New York, ISBN: 978-0023801402, 1967.
13. M. I. Friswell, John E. T. Penny, S. D. Garvey and Arthur
W. Lees, Dynamics of Rotating Machines Book,
Cambridge University Press, ISBN-10: 0521850169,
2010.
LIST OF SYMBOLS
ms sprung mass
c1,c2 damping coefficient of suspension
(1/f/11 : front and 2/r/22: rear)
k1, k2 suspension stiffness (1: front and
2: rear)
J pitch moment of inertia
xrf, xrr road excitation input to rigid model
(f: front and r: rear)
y1, y2 road excitation input to flexible
model (1: front and 2: rear)
xs bounce displacement of rigid two
dof model
y bounce displacement of CG of
flexible two dof model
θ pitch displacement of CG of
flexible two dof model
φ pitch displacement of rigid two dof
model
Vi(x) ith
mode shape
ηi(t) time response of displacement in
body fixed frame due to ith
mode
v0 initial velocity of vehicle
l1 distance of the CG from the front
end
l2 distance of the CG from the rear
end
ρ density of the chassis material
A area of cross section of chassis
E Young’s Modulus of the chassis
material
I area moment of inertia of the
chassis
L length of chassis
x1, x2 distance of the suspension from the
ends (1:front and 2:rear)
ABBREVIATIONS
Dof
Degree of freedom
CG
Centre of gravity
FRF
Frequency Response
Function
APPENDIX
Rigid two dof model simulation parameters
Table 3. Physical parameters used in the simulations of the
rigid two dof model
Sprung mass(ms) 603.043 kg
Front suspension stiffness (k1) 35000 N/m
Rear suspension stiffness(k1) 32000 N/m
Distance of CG from front (l1) 2.125 m
Distance of CG from rear(l2) 2.125 m
Front damping coefficient (c1) 2570 Ns/m
Rear damping coefficient (c2) 2480 Ns/m
Moment of inertia(J) 3630.84 kgm2
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Flexible two dof model simulation parameters
Table 4. Physical parameters used in the simulations of the
flexible two dof model
Sprung mass (ms) 603.043 kg
Front suspension stiffness (k1) 35000 N/m
Rear suspension stiffness (k2) 32000 N/m
Distance of CG from front (l1) 2.125 m
Distance of CG from rear(l2) 2.125 m
Front damping coefficient(c1) 2570 Ns/m
Rear damping coefficient(c2) 2480 Ns/m
Moment of inertia (J0) 3630.84 kgm2
Young’s Modulus (E) 210 GPa
Area moment of inertia, (I) 2.6X10-5
m4
Density, ρ 7850 kg/m3
x1&x2 0 m
Experimental setup parameters
Table 5. Physical parameters of the experimental setup
Sprung mass (ms) 1.7786 kg
Front suspension stiffness (k1) 13757 N/m
Rear suspension stiffness (k2) 13757 N/m
Distance of CG from front (l1) 0.5125 m
Distance of CG from rear(l2) 0.5125 m
Moment of inertia (J0) 0.1557 kgm2
Young’s Modulus (E) 210 GPa
Area moment of inertia, (I) 5.57X10-10
m4
Density,(ρ) 7850 kg/m3
x1 and x2 0 m