Circular plates with holes are extensively used in mechanical components. The existence of a hole
in a circular plate results in a significant change in the natural frequencies and mode shapes of the structure.
Especially if the hole is located eccentrically, the vibration behavior of these structures is expected to deviate
significantly from that of a plate with a concentric hole. These holes usually cause the change of natural
frequency as well as the decrease of load carrying capacity. It is important to comprehend the associated effects
in the work of mechanical design or flight control of the structure. Therefore, in this study, an experimental
method to determine the modal characteristics of a plate with multiple holes and slots are used is verified by the
finite element analysis (FEA) with ANSYS. Also, the relationship between parameter variations and vibration
modes is investigated. These results can be used as guidance for the modal analysis and damage detection of a
circular plate with a hole.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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.
A review and buckling analysis of stiffened plateeSAT Journals
Abstract It happens many times that the structure is safe in normal stress and deflection but fails in buckling. Buckling analysis is one of the method to go for such type of analysis.It predicts various modes of buckling. Plates are used in many applications such as structures, aerospace, automobile etc. Such structures are subjected to heavy uniformly distributed load and concentrated load many times over it’s life span. Strength of these structures are increased by adding stiffeners to its plate. This paper deals with the analysis of rectangular stiffened plates which forms the basis of structures. A comparison of stiffened plate and unstiffened plate is done for the same dimensions. In order to continue this analysis various research papers were studied to understand the previous tasks done for stiffened plate. Hyper mesh and Nastran is used in this research work.Buckling analysis is performed for the component with aspect ratio of 2.Rectangular flat bar is used as stiffener Keywords: Stiffened Plate; Dynamic load; Buckling; Aspect ratio;Buckling Analysis.
This document discusses various methods for analyzing steel space frames, including first-order elastic analysis, second-order elastic analysis, first-order inelastic (plastic) analysis, and second-order inelastic (plastic) analysis. It notes that first-order elastic analysis is commonly used but does not account for important second-order effects from frame deflections. Second-order elastic analysis more accurately considers these effects through methods like elastic buckling analysis or full second-order analysis. Advanced second-order inelastic analyses may also consider effects of plastic behavior, residual stresses, and imperfections, though they are rarely done in practice. The document explores these analysis methods in more detail.
Model Development for Estimation of Failure Loads: A Case Study of Composite ...ijsrd.com
This paper deals with the study of failure loads of glass vinylester composite plates with a circular hole subjected to a traction force by a rigid pin. These are investigated for two variables, the ratio of distance from the free edge of the plate (E) to the diameter of the hole (D) and the ratio of width of the plate (W) to the diameter of the hole (D). The work consists of a numerical study of different specimens using finite element analysis package ANSYS. Also, a mathematical model has been developed to determine the failure loads of different geometry plates. The results obtained from the numerical study and the mathematical models are compared with experimental results from the existing literature and the correlations are observed for both. A comparison of the experimental results with the numerical model shows that the numerical model gives results with correlation co-efficient 0.96. A comparison of the experimental results with the mathematical model shows that the mathematical model gives results with correlation co-efficient 0.99. For estimation of the failure loads within the range of E/D and W/D considered for the study, the mathematical model developed, i.e., Full Cubic Model proves to be more efficient with the observed values of correlation co-efficient, Root Mean Square Error and Maximum Absolute Error.
Estimating damping in structure made of different m aterials (steel,brass,aluminum) and processes sti ll remains as one of the biggest challengers. All mate rials posses certain amount of internal damping,wh ich manifested as dissipation of energy from the system . This energy in a vibratory system is either dissipated into heat or radiated away from the syst em. Material damping or internal damping contribute s to about 10-15% of total system damping. Cantilever beams of required size & shape are prepared for experimental purpose & damping ratio is investigate d. Damping ratio is determined by half-power bandwidth method. It is observed that damping ratio is higher for steel than brass than aluminum.
Finite element analysis in orthodontics/ /certified fixed orthodontic courses...Indian dental academy
The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and offering a wide range of dental certified courses in different formats.
Analysis of Isotropic Perforated Stiffened Plate Using FEMIJERA Editor
In this paper, studied the structural instability caused by circular and square perforated plate having all round simply supported and clamped plate boundary conditions subjected to inplane uniaxial compression loading and also the strengthening effect of the stiffeners when they are reinforced to the unperforated and perforated plate in longitudinal and transverse directions. The area ratios, aspect ratios and types of stiffeners are the parameters considered. A general purpose finite element analysis software ANSYS is used to carry out the study. Results show that the presence of a central circular and square perforations causes reduction in buckling strength of plate and stiffeners can be used to compensate this reduction before it can be used to its best advantage. It is also observed that the plate strengthening effect of longitudinal stiffener is more than that of transverse stiffener for both unperforated and perforated plate. An economical design is possible by introducing stiffeners of optimum size.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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.
A review and buckling analysis of stiffened plateeSAT Journals
Abstract It happens many times that the structure is safe in normal stress and deflection but fails in buckling. Buckling analysis is one of the method to go for such type of analysis.It predicts various modes of buckling. Plates are used in many applications such as structures, aerospace, automobile etc. Such structures are subjected to heavy uniformly distributed load and concentrated load many times over it’s life span. Strength of these structures are increased by adding stiffeners to its plate. This paper deals with the analysis of rectangular stiffened plates which forms the basis of structures. A comparison of stiffened plate and unstiffened plate is done for the same dimensions. In order to continue this analysis various research papers were studied to understand the previous tasks done for stiffened plate. Hyper mesh and Nastran is used in this research work.Buckling analysis is performed for the component with aspect ratio of 2.Rectangular flat bar is used as stiffener Keywords: Stiffened Plate; Dynamic load; Buckling; Aspect ratio;Buckling Analysis.
This document discusses various methods for analyzing steel space frames, including first-order elastic analysis, second-order elastic analysis, first-order inelastic (plastic) analysis, and second-order inelastic (plastic) analysis. It notes that first-order elastic analysis is commonly used but does not account for important second-order effects from frame deflections. Second-order elastic analysis more accurately considers these effects through methods like elastic buckling analysis or full second-order analysis. Advanced second-order inelastic analyses may also consider effects of plastic behavior, residual stresses, and imperfections, though they are rarely done in practice. The document explores these analysis methods in more detail.
Model Development for Estimation of Failure Loads: A Case Study of Composite ...ijsrd.com
This paper deals with the study of failure loads of glass vinylester composite plates with a circular hole subjected to a traction force by a rigid pin. These are investigated for two variables, the ratio of distance from the free edge of the plate (E) to the diameter of the hole (D) and the ratio of width of the plate (W) to the diameter of the hole (D). The work consists of a numerical study of different specimens using finite element analysis package ANSYS. Also, a mathematical model has been developed to determine the failure loads of different geometry plates. The results obtained from the numerical study and the mathematical models are compared with experimental results from the existing literature and the correlations are observed for both. A comparison of the experimental results with the numerical model shows that the numerical model gives results with correlation co-efficient 0.96. A comparison of the experimental results with the mathematical model shows that the mathematical model gives results with correlation co-efficient 0.99. For estimation of the failure loads within the range of E/D and W/D considered for the study, the mathematical model developed, i.e., Full Cubic Model proves to be more efficient with the observed values of correlation co-efficient, Root Mean Square Error and Maximum Absolute Error.
Estimating damping in structure made of different m aterials (steel,brass,aluminum) and processes sti ll remains as one of the biggest challengers. All mate rials posses certain amount of internal damping,wh ich manifested as dissipation of energy from the system . This energy in a vibratory system is either dissipated into heat or radiated away from the syst em. Material damping or internal damping contribute s to about 10-15% of total system damping. Cantilever beams of required size & shape are prepared for experimental purpose & damping ratio is investigate d. Damping ratio is determined by half-power bandwidth method. It is observed that damping ratio is higher for steel than brass than aluminum.
Finite element analysis in orthodontics/ /certified fixed orthodontic courses...Indian dental academy
The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and offering a wide range of dental certified courses in different formats.
Analysis of Isotropic Perforated Stiffened Plate Using FEMIJERA Editor
In this paper, studied the structural instability caused by circular and square perforated plate having all round simply supported and clamped plate boundary conditions subjected to inplane uniaxial compression loading and also the strengthening effect of the stiffeners when they are reinforced to the unperforated and perforated plate in longitudinal and transverse directions. The area ratios, aspect ratios and types of stiffeners are the parameters considered. A general purpose finite element analysis software ANSYS is used to carry out the study. Results show that the presence of a central circular and square perforations causes reduction in buckling strength of plate and stiffeners can be used to compensate this reduction before it can be used to its best advantage. It is also observed that the plate strengthening effect of longitudinal stiffener is more than that of transverse stiffener for both unperforated and perforated plate. An economical design is possible by introducing stiffeners of optimum size.
THREE-DIMENSIONAL STUDY FOR THE RELATIVE POSITIONING OF MECHANICAL ELEMENTS I...meijjournal
ABSTRACT
The great evolution of the data-processing tools during the last years allowed for the development of the computer aided design in the field of mechanical structures. Controlling the clearance in joints between parts, is one of the required objectives to provide accurate relative movements and to minimize geometrical errors. For that purpose, a new method of static study allowing for the computation of the equilibrium positions of various elements in spatial mechanisms constituted by parallel joints and subjected to mechanical loadings is proposed. The isostatic study takes into account the presence of the clearance in the mechanism joints. The method is based to the minimization of the potential energy by means of some algorithms of optimization. The results obtained show the effectiveness of the method.
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.
Investigations on material casualty of plates under impact load conditionseSAT Journals
This document summarizes an investigation into the material damage of plates under impact load conditions. Finite element models of tungsten fragments impacting mild steel and titanium plates were created in LS-DYNA. The kinetic energy, velocity, von mises stress, effective plastic strain, and hole diameter damage of the plates were measured for impact velocities of 300, 500, 700, and 1000 mm/ms. Higher impact velocities led to greater decreases in fragment velocity and kinetic energy upon impact, indicating more energy was absorbed by the plates. Von mises stresses and plastic strains in the plates and fragment increased only slightly with higher velocities. Greater impact velocities produced larger holes in the plates, showing higher damage.
Design and analysis of Stress on Thick Walled Cylinder with and with out HolesIJERA Editor
The conventional elastic analysis of thick walled cylinders to final radial & hoop stresses is applicable for the internal pressures up to yield strength of material. The stress is directly proportional to strain up to yield point Beyond elastic point, particularly in thick walled cylinders. The operating pressures are reduced or the material properties are strengthened. There is no such existing theory for the stress distributions around radial holes under impact of varying internal pressure. Present work puts thrust on this area and relation between pressure and stress distribution is plotted graphically based on observations. Here focus is on pure mechanical analysis & hence thermal, effects are not considered. The thick walled cylinders with a radial cross-hole ANSYS Macro program employed to evaluate the fatigue life of vessel. Stresses that remain in material even after removing applied loads are known as residual stresses. These stresses occur only when material begins to yield plastically. Residual stresses can be present in any mechanical structure because of many causes. Residual stresses may be due to the technological process used to make the component. Manufacturing processes lead to plastic deformation. Elasto plastic analysis with bilinear kinematic hardening material is performed to know the effect of hole sizes. It is observed that there are several factors which influence stress intensity factors. The Finite element analysis is conducted using commercial solvers ANSYS & CATIA. Theoretical formulae based results are obtained from MATLAB programs. The results are presented in form of graphs and tables.
This document presents a 3D finite element analysis of stress concentration factors (SCF) and deflection in thin isotropic and orthotropic plates with a central circular hole subjected to transverse loading. The effects of thickness-to-diameter (t/D) ratio and diameter-to-plate width (D/A) ratio on SCF and deflection are studied. Results show that SCF decreases with increasing D/A ratio for all materials. SCF increases with t/D ratio for most materials and stresses. Deflection increases with D/A ratio but is relatively unaffected by t/D ratio. Comparisons with 2D analyses show greater variation for orthotropic plates, indicating 2D results should not be used to
The document summarizes a finite element analysis of a torpedo battery tray conducted to evaluate its performance under severe vibration. The battery tray was modeled and meshed in ANSYS. Static, modal, harmonic and shock analyses were performed by applying loads in different axes. Results from the ANSYS simulation like deformation, stresses, natural frequencies and frequency response were compared to experimental test data. The maximum errors between simulation and experimental results for deformation and stresses were within 10%.
IRJET- Assessment of the Codal Provisions for Asymmetric BuildingsIRJET Journal
1) The document assesses the codal provisions for analyzing asymmetric buildings given in IS: 1893 (2000) using pushover analysis in SAP 2000 software.
2) It summarizes previous research on analyzing asymmetric buildings that found increased torsion, displacements, and member forces compared to symmetric buildings. Mass and stiffness eccentricity in asymmetric buildings causes increased seismic effects.
3) The study analyzes two 5-story building models - one symmetric and one asymmetric - to evaluate their seismic performance and improve the asymmetric building's torsional stability. Pushover analysis is used to conduct the evaluation.
Analysis Of Laminated and Sandwich Composites by A Zig-Zag Plate Element with...IJERA Editor
A C° layerwise plate element with standard nodal d.o.f. and serendipity interpolation functions is applied to the analysis of laminates and sandwiches giving rise to strong layerwise effects. The element is obtained using an energy updating technique and symbolic calculus starting from a physically-based zig-zag model with variable kinematics and fixed d.o.f. able to a priori satisfy to displacement and stress continuity at the material interfaces. Non classical feature, a high-order piecewise zig-zag variation of the transverse displacement is assumed as it helps keeping equilibrium. Crushing of core is studied carrying apart a detailed 3D modelling of the honeycomb structure discretizing the cell walls with plate elements, with the aim of obtaining apparent elastic moduli at each load level. Using such apparent moduli, a 2D homogenized analysis is carried out simulating sandwiches as multi-layered structures Applications are presented to plates undergoing impulsive loading incorporating plies with spatially variable stiffness properties. It is shown that accurate predictions are always obtained in in the numerical applications with a very low computational effort. Compared to kinematically based zig-zag models, present physically based one is proven to more accurate, being always in a good agreement with exact 3D solutions.
IRJET- Vibration Analysis of Simply Supported Beam with Varying Crack Dep...IRJET Journal
This document discusses using finite element analysis in ANSYS to analyze vibration in a simply supported beam with cracks of varying depth and location. It first provides background on using changes in natural frequency and mode shapes to detect damage in structures. It then reviews previous research on modeling cracks and their effects in beams. The document describes developing finite element models of cracked and uncracked beams in ANSYS to calculate natural frequencies and compare to theoretical results. The goal is to present results of using vibration analysis for crack detection.
Determination of stress intensity factor for a crack emanating from a hole inIAEME Publication
This document describes a study determining the stress intensity factor (SIF) for a crack emanating from a hole in a pressurized cylinder using the finite element method. A cylinder model with a hole and through crack is created in CATIA and imported into ANSYS for meshing and analysis. The SIF is evaluated using the displacement extrapolation method. The results show that the SIF value rises sharply when the crack tip is near the hole and stabilizes as the crack tip moves farther from the hole. The SIF values from finite element analysis agree well with theoretical equations, validating the proposed methodology.
A COMPARATIVE STUDY OF VARIOUS METHODS TO EVALUATE IMPEDANCE FUNCTION FOR SHA...Samirsinh Parmar
Impedance function, Foundation Vibration, dynamic soil-structure interaction, Barkan, Dominguez, Dobry and Gazetas for evaluation of impedance functions for various modes of vibration of shallow foundation
Crack Detection for Various Loading Conditions in Beam Using Hilbert – Huang ...IOSR Journals
The document discusses crack detection in beams using the Hilbert-Huang transform (HHT). It first provides background on using vibration-based methods to detect structural damage. It then describes modeling a cracked beam using finite element analysis, representing the crack as a rotational spring. Vibration analysis is performed on simply supported, fixed-fixed, free-free, and cantilever beams with cracks. HHT is applied to the transformed response to determine crack location based on changes in spatial variation. Both analytical and experimental results show good agreement with the model and that HHT is effective for analysis.
Fem /certified fixed orthodontic courses by Indian dental academy Indian dental academy
The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and offering a wide range of dental certified courses in different formats.
Indian dental academy provides dental crown & Bridge,rotary endodontics,fixed orthodontics,
Dental implants courses.for details pls visit www.indiandentalacademy.com ,or call
0091-9248678078
Finite element analysis in orthodontics /certified fixed orthodontic courses ...Indian dental academy
The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and offering a wide range of dental certified courses in different formats.
Indian dental academy provides dental crown & Bridge,rotary endodontics,fixed orthodontics,
Dental implants courses.for details pls visit www.indiandentalacademy.com ,or call
0091-9248678078
Probabilistic Design of Hollow Circular Composite Structure by using Finite E...IJERA Editor
This document summarizes a study that uses finite element analysis to analyze the bending stress of a hollow circular composite beam under static loading conditions while accounting for uncertainty in design variables. A probabilistic design system is used to simulate the effects of varying the beam's length, radius, material properties, ply angles, thickness, and applied load on the bending stress. The results identify that variation in load, radius, modulus, ply thickness, and angles have the most significant effect on bending stress. The analysis finds the bending stress can range from 104 to 392 MPa with a 90% probability of being below 250 MPa. Improving the robustness of the design may require addressing variables with the highest sensitivity on bending stress.
This document describes a modal analysis workshop problem to find the first five natural frequencies and mode shapes of a flat rectangular plate with fixed-free boundary conditions. It provides the model dimensions and material properties, describes generating a finite element model in MSC/Nastran with shell elements, applying boundary conditions to one edge, and performing a normal modes analysis to obtain the natural frequencies and mode shapes. The objective is to have students manually create the finite element input file to model the plate and complete the modal analysis.
Numerical parametric study on interval shift variation in simo sstd technique...eSAT Journals
This document presents a parametric study on the time shift interval variation in the SIMO-SSTD technique for experimental modal analysis. The SSTD (Single Station Time Domain) technique extracts modal parameters from free decay responses without using Fourier transforms. The study investigates the accuracy of natural frequency and damping ratio results from the SSTD algorithm when using different time shift intervals between data matrices. Simulated data with known modal properties is used to calculate percentage errors for different shift intervals and noise levels. The goal is to determine the effect of time shift interval on the accuracy of the SSTD technique.
Modal and harmonic analysis of tapered composite iSRINIVASULU N V
This document presents the results of a modal and harmonic analysis of a tapered composite I-beam with its big end fixed and small end free. The natural frequencies and mode shapes are investigated for various fiber orientations in the top and bottom flanges and web of the beam, as well as different modulus ratios. The natural frequencies are found to increase with increasing fiber angle and modulus ratio. Harmonic analysis applying a 1N load at the free end shows the displacement decreases with increasing natural frequency for different fiber angles and modulus ratios.
Operational Modal Analysis Implementation on a Hybrd Composite PlateHazira Haidzir
This document discusses modal analysis techniques for predicting structural deformation in aerospace structures due to airflow. It compares experimental modal analysis (EMA), which uses artificial excitation, to operational modal analysis (OMA), which extracts modal properties from operational response only. The study implemented OMA on a composite plate using a laser vibrometer for contactless response measurement. OMA results matched an EMA analysis using impact testing, validating the technique. OMA avoids complex artificial excitation and represents actual operating conditions.
Example: Modal analysis using DIgSILENT PowerFactory. This example shows the application modal analysis with Power Factory to P.M. Anderson Test System
THREE-DIMENSIONAL STUDY FOR THE RELATIVE POSITIONING OF MECHANICAL ELEMENTS I...meijjournal
ABSTRACT
The great evolution of the data-processing tools during the last years allowed for the development of the computer aided design in the field of mechanical structures. Controlling the clearance in joints between parts, is one of the required objectives to provide accurate relative movements and to minimize geometrical errors. For that purpose, a new method of static study allowing for the computation of the equilibrium positions of various elements in spatial mechanisms constituted by parallel joints and subjected to mechanical loadings is proposed. The isostatic study takes into account the presence of the clearance in the mechanism joints. The method is based to the minimization of the potential energy by means of some algorithms of optimization. The results obtained show the effectiveness of the method.
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.
Investigations on material casualty of plates under impact load conditionseSAT Journals
This document summarizes an investigation into the material damage of plates under impact load conditions. Finite element models of tungsten fragments impacting mild steel and titanium plates were created in LS-DYNA. The kinetic energy, velocity, von mises stress, effective plastic strain, and hole diameter damage of the plates were measured for impact velocities of 300, 500, 700, and 1000 mm/ms. Higher impact velocities led to greater decreases in fragment velocity and kinetic energy upon impact, indicating more energy was absorbed by the plates. Von mises stresses and plastic strains in the plates and fragment increased only slightly with higher velocities. Greater impact velocities produced larger holes in the plates, showing higher damage.
Design and analysis of Stress on Thick Walled Cylinder with and with out HolesIJERA Editor
The conventional elastic analysis of thick walled cylinders to final radial & hoop stresses is applicable for the internal pressures up to yield strength of material. The stress is directly proportional to strain up to yield point Beyond elastic point, particularly in thick walled cylinders. The operating pressures are reduced or the material properties are strengthened. There is no such existing theory for the stress distributions around radial holes under impact of varying internal pressure. Present work puts thrust on this area and relation between pressure and stress distribution is plotted graphically based on observations. Here focus is on pure mechanical analysis & hence thermal, effects are not considered. The thick walled cylinders with a radial cross-hole ANSYS Macro program employed to evaluate the fatigue life of vessel. Stresses that remain in material even after removing applied loads are known as residual stresses. These stresses occur only when material begins to yield plastically. Residual stresses can be present in any mechanical structure because of many causes. Residual stresses may be due to the technological process used to make the component. Manufacturing processes lead to plastic deformation. Elasto plastic analysis with bilinear kinematic hardening material is performed to know the effect of hole sizes. It is observed that there are several factors which influence stress intensity factors. The Finite element analysis is conducted using commercial solvers ANSYS & CATIA. Theoretical formulae based results are obtained from MATLAB programs. The results are presented in form of graphs and tables.
This document presents a 3D finite element analysis of stress concentration factors (SCF) and deflection in thin isotropic and orthotropic plates with a central circular hole subjected to transverse loading. The effects of thickness-to-diameter (t/D) ratio and diameter-to-plate width (D/A) ratio on SCF and deflection are studied. Results show that SCF decreases with increasing D/A ratio for all materials. SCF increases with t/D ratio for most materials and stresses. Deflection increases with D/A ratio but is relatively unaffected by t/D ratio. Comparisons with 2D analyses show greater variation for orthotropic plates, indicating 2D results should not be used to
The document summarizes a finite element analysis of a torpedo battery tray conducted to evaluate its performance under severe vibration. The battery tray was modeled and meshed in ANSYS. Static, modal, harmonic and shock analyses were performed by applying loads in different axes. Results from the ANSYS simulation like deformation, stresses, natural frequencies and frequency response were compared to experimental test data. The maximum errors between simulation and experimental results for deformation and stresses were within 10%.
IRJET- Assessment of the Codal Provisions for Asymmetric BuildingsIRJET Journal
1) The document assesses the codal provisions for analyzing asymmetric buildings given in IS: 1893 (2000) using pushover analysis in SAP 2000 software.
2) It summarizes previous research on analyzing asymmetric buildings that found increased torsion, displacements, and member forces compared to symmetric buildings. Mass and stiffness eccentricity in asymmetric buildings causes increased seismic effects.
3) The study analyzes two 5-story building models - one symmetric and one asymmetric - to evaluate their seismic performance and improve the asymmetric building's torsional stability. Pushover analysis is used to conduct the evaluation.
Analysis Of Laminated and Sandwich Composites by A Zig-Zag Plate Element with...IJERA Editor
A C° layerwise plate element with standard nodal d.o.f. and serendipity interpolation functions is applied to the analysis of laminates and sandwiches giving rise to strong layerwise effects. The element is obtained using an energy updating technique and symbolic calculus starting from a physically-based zig-zag model with variable kinematics and fixed d.o.f. able to a priori satisfy to displacement and stress continuity at the material interfaces. Non classical feature, a high-order piecewise zig-zag variation of the transverse displacement is assumed as it helps keeping equilibrium. Crushing of core is studied carrying apart a detailed 3D modelling of the honeycomb structure discretizing the cell walls with plate elements, with the aim of obtaining apparent elastic moduli at each load level. Using such apparent moduli, a 2D homogenized analysis is carried out simulating sandwiches as multi-layered structures Applications are presented to plates undergoing impulsive loading incorporating plies with spatially variable stiffness properties. It is shown that accurate predictions are always obtained in in the numerical applications with a very low computational effort. Compared to kinematically based zig-zag models, present physically based one is proven to more accurate, being always in a good agreement with exact 3D solutions.
IRJET- Vibration Analysis of Simply Supported Beam with Varying Crack Dep...IRJET Journal
This document discusses using finite element analysis in ANSYS to analyze vibration in a simply supported beam with cracks of varying depth and location. It first provides background on using changes in natural frequency and mode shapes to detect damage in structures. It then reviews previous research on modeling cracks and their effects in beams. The document describes developing finite element models of cracked and uncracked beams in ANSYS to calculate natural frequencies and compare to theoretical results. The goal is to present results of using vibration analysis for crack detection.
Determination of stress intensity factor for a crack emanating from a hole inIAEME Publication
This document describes a study determining the stress intensity factor (SIF) for a crack emanating from a hole in a pressurized cylinder using the finite element method. A cylinder model with a hole and through crack is created in CATIA and imported into ANSYS for meshing and analysis. The SIF is evaluated using the displacement extrapolation method. The results show that the SIF value rises sharply when the crack tip is near the hole and stabilizes as the crack tip moves farther from the hole. The SIF values from finite element analysis agree well with theoretical equations, validating the proposed methodology.
A COMPARATIVE STUDY OF VARIOUS METHODS TO EVALUATE IMPEDANCE FUNCTION FOR SHA...Samirsinh Parmar
Impedance function, Foundation Vibration, dynamic soil-structure interaction, Barkan, Dominguez, Dobry and Gazetas for evaluation of impedance functions for various modes of vibration of shallow foundation
Crack Detection for Various Loading Conditions in Beam Using Hilbert – Huang ...IOSR Journals
The document discusses crack detection in beams using the Hilbert-Huang transform (HHT). It first provides background on using vibration-based methods to detect structural damage. It then describes modeling a cracked beam using finite element analysis, representing the crack as a rotational spring. Vibration analysis is performed on simply supported, fixed-fixed, free-free, and cantilever beams with cracks. HHT is applied to the transformed response to determine crack location based on changes in spatial variation. Both analytical and experimental results show good agreement with the model and that HHT is effective for analysis.
Fem /certified fixed orthodontic courses by Indian dental academy Indian dental academy
The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and offering a wide range of dental certified courses in different formats.
Indian dental academy provides dental crown & Bridge,rotary endodontics,fixed orthodontics,
Dental implants courses.for details pls visit www.indiandentalacademy.com ,or call
0091-9248678078
Finite element analysis in orthodontics /certified fixed orthodontic courses ...Indian dental academy
The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and offering a wide range of dental certified courses in different formats.
Indian dental academy provides dental crown & Bridge,rotary endodontics,fixed orthodontics,
Dental implants courses.for details pls visit www.indiandentalacademy.com ,or call
0091-9248678078
Probabilistic Design of Hollow Circular Composite Structure by using Finite E...IJERA Editor
This document summarizes a study that uses finite element analysis to analyze the bending stress of a hollow circular composite beam under static loading conditions while accounting for uncertainty in design variables. A probabilistic design system is used to simulate the effects of varying the beam's length, radius, material properties, ply angles, thickness, and applied load on the bending stress. The results identify that variation in load, radius, modulus, ply thickness, and angles have the most significant effect on bending stress. The analysis finds the bending stress can range from 104 to 392 MPa with a 90% probability of being below 250 MPa. Improving the robustness of the design may require addressing variables with the highest sensitivity on bending stress.
This document describes a modal analysis workshop problem to find the first five natural frequencies and mode shapes of a flat rectangular plate with fixed-free boundary conditions. It provides the model dimensions and material properties, describes generating a finite element model in MSC/Nastran with shell elements, applying boundary conditions to one edge, and performing a normal modes analysis to obtain the natural frequencies and mode shapes. The objective is to have students manually create the finite element input file to model the plate and complete the modal analysis.
Numerical parametric study on interval shift variation in simo sstd technique...eSAT Journals
This document presents a parametric study on the time shift interval variation in the SIMO-SSTD technique for experimental modal analysis. The SSTD (Single Station Time Domain) technique extracts modal parameters from free decay responses without using Fourier transforms. The study investigates the accuracy of natural frequency and damping ratio results from the SSTD algorithm when using different time shift intervals between data matrices. Simulated data with known modal properties is used to calculate percentage errors for different shift intervals and noise levels. The goal is to determine the effect of time shift interval on the accuracy of the SSTD technique.
Modal and harmonic analysis of tapered composite iSRINIVASULU N V
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Limit States Solution to CSCS Orthotropic Thin Rectangular Plate Carrying Tra...ijtsrd
The analysis of thin rectangular orthotropic plate with two opposite edges clamped and the other two opposite edges simply supported CSCS , carrying transverse loads was investigated in this study. The Ritz total potential energy functional was used. The minimization of the total potential energy functional produces the expression for the coefficient of deflection. The coefficient of deflection was used to obtain equation for the maximum lateral load of an orthotropic thin rectangular plate based on allowable deflection. Also, equation for the maximum lateral load of an orthotropic thin rectangular plate based on allowable stress was developed.Developed stiffness coefficients were substituted in the lateral load equations to obtain the maximum lateral load values for a CSCS plate. Numerical examples using permissible deflection of 10mm and yield strength of 250MPa, plate thickness varying from 5mm to 12.5 mm with 0.5mm intervals were done to determine the maximum lateral loads corresponding to an orthotropic thin rectangular CSCS plate carrying transverse loads when n1 = Ey Ex = 0.7 and n2 = G Ex = 0.41 for aspect ratios b a of 1.0, 1.25 and 1.50. Bertram D. I. | Okere C. E. | Ibearugbulem O. M. | Nwokorobia G. C. "Limit States Solution to CSCS Orthotropic Thin Rectangular Plate Carrying Transverse Loads" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-6 , October 2021, URL: https://www.ijtsrd.com/papers/ijtsrd47566.pdf Paper URL : https://www.ijtsrd.com/engineering/civil-engineering/47566/limit-states-solution-to-cscs-orthotropic-thin-rectangular-plate-carrying-transverse-loads/bertram-d-i
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Study on Effect of Crack Inclination and Location on Natural Frequency for In...IRJET Journal
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Free Vibrational Analysis of Cracked RC Beam- A ReviewIRJET Journal
This document reviews research on analyzing the effect of cracks on the vibrational properties of reinforced concrete beams. It begins with an abstract describing how cracks can change the physical characteristics and dynamic response of structures. The objective is to study how the natural frequency and mode shapes of cracked beams vary with crack depth and inclination using finite element analysis in ANSYS. It then provides background on vibrational analysis, beam cracking, and literature reviewing past studies on using natural frequencies to detect structural damage.
Higher Order Normal Shear Deformation Theory for Static FG Rectangular PlatesIRJET Journal
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First order shear deformation (FSDT) theory for laminated composite beams is used to study free vibration of
laminated composite beams, and finite element method (FEM) is employed to obtain numerical solution of the
governing differential equations. Free vibration analysis of laminated beams with rectangular cross – section for
various combinations of end conditions is studied. To verify the accuracy of the present method, the frequency
parameters are evaluated and compared with previous work available in the literature. The good agreement with
other available data demonstrates the capability and reliability of the finite element method and the adopted beam
model used.
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Free Vibration Analysis of circular plates with holes and cutouts
1. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)
e-ISSN: 2278-1684,p-ISSN: 2320-334X, Volume 8, Issue 2 (Jul. - Aug. 2013), PP 46-54
www.iosrjournals.org
www.iosrjournals.org 46 | Page
Free Vibration Analysis of circular plates with holes and cutouts
Shrikant B. Thakare1
, Prof. A. V. Damale2
1
(PG Student, Department of mechanical Engg, SRES COE, University of Pune, Maharashtra, India)
2
(Asst. Professor, Department of mechanical Engg, SRES COE, University of Pune, Maharashtra, India)
Abstract : Circular plates with holes are extensively used in mechanical components. The existence of a hole
in a circular plate results in a significant change in the natural frequencies and mode shapes of the structure.
Especially if the hole is located eccentrically, the vibration behavior of these structures is expected to deviate
significantly from that of a plate with a concentric hole. These holes usually cause the change of natural
frequency as well as the decrease of load carrying capacity. It is important to comprehend the associated effects
in the work of mechanical design or flight control of the structure. Therefore, in this study, an experimental
method to determine the modal characteristics of a plate with multiple holes and slots are used is verified by the
finite element analysis (FEA) with ANSYS. Also, the relationship between parameter variations and vibration
modes is investigated. These results can be used as guidance for the modal analysis and damage detection of a
circular plate with a hole.
Keywords: circular plate, FEA, modal analysis, natural frequencies, vibration.
I. Introduction
The Circular plates with multiple circular holes are widely used in engineering structures, e.g. missiles,
aircraft, etc., either to reduce the weight of the structure, to increase the range of inspection or to satisfy other
engineering applications. These holes in a structure usually invoke natural frequency change and loading
capacity decrease. It is important to comprehend the corresponding effects in the process of mechanical design.
As quoted by Leissa and Narita’’The free vibrations of circular plates have been of practical and
academic interest for at least a century and a half’’, over the past few decades, most of the researches have
focused on the analytical solutions for natural frequencies of the circular or annular plates.
Circular and annular plates with variable thickness are widely used in many engineering structures and
machines. By appropriate variation of plate thickness, these plates can have significantly greater efficiency for
vibration as compared to the plates of uniform thickness and also provide the advantage of reduction in weight
and size.
The objective of current work is study of the behavior of circular plates with free boundary condition
but having different working conditions such as numbers of holes, aspect ratio, and effect of radial slots/cutouts
and with diff thickness of plate is important, as used in several machine components, such as circular saw
blades, Disc brake plates, Diaphragm springs etc. The knowledge of natural frequencies of component is of
great interest in the analysis of response of structures to various excitations. Unwanted noise, vibration &
accidental failure associated with the operation has become an important economic and technological problem
in the industry that can be studied by this work.
ANSYS/CAE is a general purpose finite element analysis tool with a group of engineering simulation
programs capable of modelling structures under different loading conditions. It can solve problems of relatively
simple structural analysis to the most complicated linear to nonlinear analyses. In a nonlinear analysis
ANSYS/CAE automatically chooses appropriate load increments and convergence tolerances and continually
adjusts them during the analysis to ensure that an accurate solution is obtained. ANSYS /CAE consist of a
widespread library of elements, wherein any type of geometry can be modelled. Apart from solving structural
problems, it can also solve problems in other different areas like fracture mechanics, soil mechanics, static
analysis, piezoelectric analysis, coupled thermal-electrical analyses, heat problems, and acoustics etc.
II. Review Of Literature
Many researchers have studied the vibration of annular plates over a long period of time. Dynamic
characteristics of annular plates are of considerable importance in many designs. Circular plates with cutouts are
extensively used in mechanical structures. Vibration analysis of this kind of structure is the foundation for
structural parameter identification, damage detection and vibration control. In general, most research work has
focused on vibration analysis of circular plates with a central hole, i.e., annular plates, and has led to a rapid
development of analytical or experimental methods, such as the energy approach, the mode subtraction
approach, etc.
Early studies have been reviewed by Leissa. [1] The monograph contains a detailed review of the
investigations on the vibration of plates of various shapes, including circular and elliptical planforms. In
2. Free Vibration Analysis of circular plates with holes and cutouts
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subsequent articles, Leissa provides information on plate vibration including different complicating effects.
Although there are many papers on the vibration of elliptical and circular plates, they refer mainly to
isotropic and polar orthotropic material.
L. Cheng et.al. [2] Attempts to reveal the relationship between parameter variations (eccentricity, hole size,
boundary condition) and vibration modes, and to discover the vibration behavior around the eccentric hole. To
our knowledge, these results are new and give guidance for the modal analysis and damage detection and the
effects of the eccentricity, whole size and boundary conditions on DMSs are investigated systematically.
Weisensel G. N. [3] has discussed the results of an extensive literature search and review of available
sources of numerical natural frequency information for stationary circular and annular elastic plates. In addition
to source information is given regarding the specific plate theory, boundary conditions, geometric properties and
material properties used to determine the natural frequency information Sources of information are tabulated
according to the above parameters for easy reference and selection of desired information This information may
be particularly useful to experts and designers when frequency data are required without the need for detailed
analysis.
Wook Kang et.al. [4] in their work, attempts were made to derive the explicit closed form solution to
mode shapes and its natural frequencies with rather good accuracy. For circular plate such as tree disk, the
simply supported and clamped boundary conditions are practically rather difficult for realization compared to
completely free ones. Therefore, this study deals only with completely free cases. It will explore the feasibility
of direct identification of elastic constants of both polar orthotropic and isotropic plates. The result from this
study can be used for parametric studies for dynamic behaviors and nondestructive material evaluation during
the initial design process.
Z.H. Zhou et.al. [5] In the present study the symplectic expansion is used to obtain the natural modes of
the Kirchhoff circular and annular plates. With the aid of Hamiltonian principle of mixed energy, a set of
Hamiltonian dual equations are obtained. The differential eigenvalue problem is then solved using the separation
of variables. The solution is expanded in terms of the symplectic adjoint orthogonal Eigen solutions with
coefficients to be determined by the boundary conditions. Numerical comparisons to the classical solutions in
literature are presented to validate the efficiency and accuracy of the symplectic method. The natural
frequencies are calculated for these plates with all possible combinations of free, clamped and simply supported
boundary conditions and inner-to-outer radius ratios. These results can be used to validate the accuracy of other
numerical method as benchmark values.
III. Finite Element Analysis (Fea) Technique Using Ansys/Cae
ANSYS/CAE is a general purpose finite element analysis tool with a group of engineering simulation
programs capable of modelling structures under different loading conditions. It can solve problems of relatively
simple structural analysis to the most complicated linear to nonlinear analyses. In a nonlinear analysis
ANSYS/CAE automatically chooses appropriate load increments and convergence tolerances and continually
adjusts them during the analysis to ensure that an accurate solution is obtained. ANSYS /CAE consist of a
widespread library of elements, wherein any type of geometry can be modelled. Apart from solving structural
problems, it can also solve problems in other different areas like fracture mechanics, soil mechanics, static
analysis, piezoelectric analysis, coupled thermal-electrical analyses, heat problems, and acoustics etc. In this
analytical framework, ANSYS /CAE is used for evaluating the frequencies, displacements and mode shapes of
the model of a cracked plate to investigate the theoretical predictions. The required inputs for the ANSYS /CAE
finite element analysis consists of model geometry, material properties, loading, boundary conditions, and an
initial crack configuration.
3.1 Theoretical analysis -
Fig. 3.1.1 circular plate with uniform thickness
3. Free Vibration Analysis of circular plates with holes and cutouts
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Rayleigh or Love is perhaps the best prime sources for the governing equations and the correct forms
of all the boundary conditions. These references are cited by Southwell but later authors consider the equations
as common knowledge. The differential equation in polar coordinates, {r, θ}, governing the axial displacement
of the plate, w, is
2
4
2
0
w
D w
t
(1)
Which when written in extenso becomes:
22 2 2
2 2 2 2
1 1
0
w
D w
r r r r r t
(2)
Where, t = time,
ρ = density of the plate material;
w = plate displacement;
2
3 1
Eh
D
: Which might be called flexural rigidity;
E = Young's modulus,
υ = Poisson's ratio and with
2h = the thickness of the plate (so h is the half thickness)
The boundary conditions (Rayleigh,) are
For zero displacement: w = 0 …2a
For encastred edge, i.e., with zero slope of the plate: ∂w/∂r = 0 …2b
A vibrating solution is assumed with displacement varying sinusoidally with azimuth.
Set
sin sinw W n t
(3)
Where ω is natural frequency.
This separation of variables leads to
2 2
4
2 2
1
0W W
r r r r
(4)
With
2 2
4
2
3 1
Eh D
(5)
W. T. Norris and J. E. T. Penny have given values of 2
a for various ratios of outer radius to inner radius
and different mode characteristics. First six harmonics are given in order for aspect ratio (b/a=0.1).
2
a Is non-dimensional frequency parameter used to calculate natural frequencies of circular plate.
2
2 2
2
3 1
a a
Eh
(6)
Where,
h = half thickness in mm
E = Young’s modulus N/m2
= Density of the cutter material in kg/m3
= frequency in rad/s.
= Poisson’s ratio taken as 0.3
a = Outer radius of cutter in mm
3.2 Modal Analysis:
Same set of command is used for modal analysis that used in any other type of finite element analysis.
Likewise, choose similar option from the graphical user interface (GUI) to build and solve models. Modal
analysis determines the vibration characteristics (natural frequencies and mode shapes) of a structure or machine
components. Experimental modal analysis of a system, deals with determination of natural frequencies, damping
4. Free Vibration Analysis of circular plates with holes and cutouts
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ratios, and mode shapes through the vibration testing. In the case of forced vibration, the analysis includes the
study of acceleration, velocity and displacement responses of the systems.
Modal analysis is the identification of vibration characteristics of elastic structures. It consists of
describing a system by its modal parameters; natural frequencies, natural damping and natural modes. This
study enables better understanding of the vibration phenomenon encountered in engineering; its purpose is to get
data from experiment in order to determine system characteristics. One can use the data in several ways,
depending on the aims to reach.
A reason to make measurements on a real test structure is the need to compare the experimental
vibration with the data produced by a simulation program like a FEM program, for instance. The aim is the
validation of theoretical model before its further use, with more; complex excitation like shocks or step changes.
Another way of using the information provided by modal analysis is to obtain a frequency response
function (FRF) from the theoretical model and real test structure and to compare both results this comparison
allows, correcting the model to a certain extent by using a trial and error approach. Modal analysis can be used
to quantitatively describe a mechanical element that will have to be part of bigger assembly. Accurate data is
required for natural frequencies, damping and mode shapes. This is referred to as a sub structuring process and
is in theoretical analysis of complex structures. This method can also be used to predict the vibration behavior of
a machinery element that has to be modified for any reason including the one of modifying the vibration
properties themselves by reducing the amplitude of vibration at a given frequency or by shifting the resonance
frequency of a given mode. Another application for modal testing is that of force determination. Given a
theoretical model and measured vibration on a real structure, it is possible to determine the forces that act upon
the real structure. Nevertheless this method is very sensitive to modeling inaccuracies and little errors can have
huge consequences. Accurate Modal Analysis requires understanding of the theoretical basis of vibration,
accurate measurement of vibration, careful and detailed data analysis.
3.2.1 Steps of Modal Analysis:
1. Modeling
Modeling includes the making of model geometry or to import the geometry from another software
package in the working environment.
2. Model meshing
This step includes the job name and analysis title and then defines the element types, element real
constant, material properties, and the model geometry.
3. Loadings
In this step, define analysis types and options, apply load, and satisfy load step options to get the finite
element solution for the natural frequency.
4. Expansion of the modes
Specify the number of mode that, you have to expand. If frequency range is selected, only modes
within that range mode results are appeared.
5. Results
Results from modal analysis are written to the structural results file. Results consist of natural
frequency, mode shapes relative stress and force distribution. Those results wish to see, database must contain
the same modal for which the solution was calculated.
IV. Observations And Fea Analysis
The specimens of circular annular plate of S.S. are chosen for testing. Following are the material
properties for the specimen plates. Young’s modulus (E) = 2.1 X 1011 N/m2, Poisson’s ratio (µ) = 0 .3, Density
of material (ρ) = 7850 N/m3. The structure is axi-symmetric and formed of an isotropic homogeneous elastic
material. Three dimensional parameters represent the disk's inner radius (b), outer radius (a) and thickness (h)
respectively. Specimens with variable thickness, aspect ratios, slot end hole size, no. of holes, are chosen for
test. These specimen sizes are chosen to facilitate the measurements by using the same fixture for all the
specimens. As boundary conditions for plate specimens are inner edge fixed and outer edge free. The FEA
analysis is done on the ANSYS software and following results were obtain which are tabulated as follows,
Case 1- For Variable Aspect ratio
TABLE 3.4.1 Result table for test specimen 1
Specimen Aspect ratio b/a
Inner diameter in
mm
Outer diameter
in mm
Number of
holes or slots
Plate 1 0.182 20 110 0
Natural Frequencies by FEA 724.33 726 780.27 963.8
Plate 2 0.4 20 50 0
Natural Frequencies by FEA 5484.0 5516.8 5529.5 6254.5
5. Free Vibration Analysis of circular plates with holes and cutouts
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Fig 3.4.1 Mode shape for aspect ratio 0.182 Fig 3.4.2 Mode shape for aspect ratio 0.4
Case 2- For Variable thickness
TABLE 3.4.2 Result table for test specimen 2
Specimen Aspect ratio b/a
Inner diameter
in mm
Outer diameter
in mm
Thickness of
plates in mm
Plate 1 0.182 20 110 1.5
Natural Frequencies by FEA 724.33 726 780.27 963.8
Plate 3 0.182 20 110 3
Natural Frequencies by FEA 1443 1445.3 1561.3 1910.3
Fig 3.4.3 Mode shape for Thickness 1.5 mm Fig 3.4.4 Mode shape for Thickness 3 mm
Case 3 - For No. of Holes in plate
TABLE 3.4.3 Result table for test specimen 3
Specimen
Aspect ratio
b/a
Inner
diameter in
mm
Outer
diameter in
mm
Number of
holes
Dia. Of
holes in
mm
Plate 1 0.182 20 110 0 0
Natural Frequencies by
FEA
724.33 726 780.27 963.8 965
Plate 4 0.182 20 110 9 10
Natural Frequencies by
FEA
594 594.68 640.34 787.41 788.10
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Fig 3.4.5 Mode shape for plates without holes Fig 3.4.6 Mode shape for plates with 9 holes
Case 4- For Variable diameter of Holes in plate
TABLE 3.4.4 Result table for test specimen 4
Specimen
Aspect
ratio b/a
Inner diameter
in mm
Outer diameter
in mm
Number
of holes
Dia. Of
holes in mm
Plate 4 0.182 20 110 9 5
Natural Frequencies by FEA 571.86 572.68 623.19 774.19 775.03
Plate 5 0.182 20 110 9 10
Natural Frequencies by FEA 594 594.68 640.34 787.41 788.10
Fig 3.4.7 Mode shape for plates with 9 holes of 10 mm &5 mm diameter
Case 5- For No. of slots in plate
Table 3.4.5 Result table for test specimen 5
Specimen
Aspect
ratio b/a
Inner
diameter in
mm
Outer diameter
in mm
Number of
slots of length
17.5 mm.
slot end
hole
dia.mm
Plate 6 0.182 20 110 9 5
Natural Frequencies by FEA 602 695 1014 1427 2311
Plate 7 0.182 20 110 10 5
Natural Frequencies by FEA 851 953 1255 1677 1917
7. Free Vibration Analysis of circular plates with holes and cutouts
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Fig. 3.4.8 Mode shape for plates with 9 radial slot & diff. slot end diameter
Case 6- For variable dia. of slot end in plate
Table 3.4.6 Result table for test specimen 6
Specimen
Aspect
ratio b/a
Inner
diameter in
mm
Outer diameter
in mm
Number of slots
of length 17.5
mm.
slot end
hole dia.mm
Plate 7 0.182 20 110 10 5
Natural Frequencies
by FEA
851 953 1255 1677 1917
Plate 8 0.182 20 110 10 10
Natural Frequencies
by FEA
828 909 1087 1316 1421
V. Result And Discussion
On the basis of the FEA analysis by using the ANSYS software analysis of vibration characteristics of
circular plates with free boundary condition but having different numbers of holes, aspect ratio, effect of radial
slots/cutouts and with diff thickness of plate is done& the following results are predicted.
Case 1- For Variable Aspect ratio
As the Aspect ratio is increases the natural frequency is increases. 100% increment in the aspect ratio gives 648
% to 757 % increase in natural frequency variable as per modes.
Fig 5.1 Comparison of natural frequency for Variable Aspect ratio
Case 2- For Variable thickness
As the thickness is increases the natural frequency is increases. 100% increment in the thickness gives
200% increase in natural frequency variable as per modes.
8. Free Vibration Analysis of circular plates with holes and cutouts
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Fig 5.2 Comparison of natural frequency for Variable thickness
Case 3- For No. of Holes in plate
Natural frequency decreases if air cooling holes are added to circular annular plates. As the holes are
introduced in the plate it reduces the natural frequency. Compare with the plate without holes the frequency is
reduced by122%.
Fig 5.3 Comparison of natural frequency for No. of Holes in plate
Case 4- For Variable diameter of Holes in plate
Natural frequency decreases if air cooling holes are added to circular annular plates. Also as the
diameter of the air cooling holes is changed the natural frequency is reduced by 103%,
Fig 5.4 Comparison of natural frequency for Variable diameter of Holes in plate
Case 5- For No. of slots in plate
Natural frequency increases as the no. of radial slots increases. 10% change in the no. of radial slots
gives 7% to 40% change in natural frequency variable as per modes.
Fig 5.5 Comparison of natural frequency for No. of slots in plate
9. Free Vibration Analysis of circular plates with holes and cutouts
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Case 6- For variable diameter of slot end in plate
Natural frequency decreases as crack end hole diameter increases. 3 to34% reductions in natural
frequency is achieved by 100% enlargement of crack end whole diameter.
Fig 5.6 Comparison of natural frequency for variable diameter of slot end in plate
VI. Conclusion
The main thrust of the work is towards the understanding of the vibration behavior of plates with diff
conditions for circular saw blades and disc brake plates in static condition. Analysis of vibration characteristics
of circular plates with free boundary condition but having different numbers of holes, aspect ratio, thickness and
effect of radial slots/cutouts are done with the FEM analysis and the results are predicted. Depending on the
various conditions the results are concluded.
Conclusion on various specimens for different conditions are obtain as, For variable Aspect ratio, As
the Aspect ratio is increases the natural frequency is increases. For variable Thickness of plates, As the thickness
is increases the natural frequency is increases. For Variable No. of Holes in plate, Natural frequency decreases if
air cooling holes are added to circular annular plates. For Variable diameter of Holes in plate, As the diameter of
the air cooling holes is changed the natural frequency is reduced. For No. of slots in plate, Natural frequency
increases as the no. of radial slots increases. for variable dia. of slot end in plate, natural frequency decreases as
crack end hole diameter increases.
References
[1] A.W. Leissa, The Shock and Vibration Digest (Plate vibration research, 1981).
[2] L. Cheng, et.al. Vibration analysis of annular-like plates, Journal of Sound and Vibration, vol. 262, pp. (2003), 1153–1170.
[3] Weisensel G. N, Natural Frequency Information for Circular and Annular Plates, Journal of Sound and Vibration,) vol. 133(l),
(1989), 129-134.
[4] Wook Kang & et.al, Approximate closed form solutions for free vibration of polar orthotropic circular plates, Journal of Applied
Acoustics, vol. 66 (2005), 1162–1179.
[5] Z.H.Zhou et.al, Natural vibration of circular and annular thin plates by Hamiltonian approach, Journal of Sound and Vibration,
vol.330, (2011), 1005–1017.