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Thesis Title:
Development of an Auto Impact Excitation Device for Operational Modal Testing (Control & Testing)
Supervisor: Dr. Ong Zhi Chao
Grade: A -
I was very grateful for my supervisor's guidance, seriously. He is one of the best lecturers I ever met in UM.
Sharing with you my dear readers who may find it useful.
Feel free to connect with me at maxermesilliam@gmail.com.
A Novel Displacement-amplifying Compliant Mechanism Implemented on a Modified...IJECEIAES
The micro-accelerometers are devices used to measure acceleration. They are implemented in applications such as tilt-control in spacecraft, inertial navigation, oil exploration, etc. These applications require high operating frequency and displacement sensitivity. But getting both high parameter values at the same time is difficult, because there are physical relationships, for each one, where the mass is involved. When the mass is reduced, the operating frequency is high, but the displacement sensitivity decreases and vice versa. The implementation of Displacement-amplifying Compliant Mechanism (DaCM) supports to this dependence decreases. In this paper the displacement sensitivity and operation frequency of a Conventional Capacitive Accelerometer are shown (CCA). A Capacitive Accelerometer with Extended Beams (CAEB) is also presented, which improves displacement sensitivity compared with CCA, and finally the implementation of DACM´s in the aforementioned devices was also carried out. All analyzed cases were developed considering the in-plane mode. The Matlab code used to calculate displacement sensitivity and operating frequency relationship is given in Appendix A.
Modeling and Estimation of Stationary and Non-stationary Noises of Rubidium A...IJERA Editor
Noise estimation of atomic clock is one of the important research areas in the field of atomic clock development and application. Most of the atomic clocks are having random-stochastic noises and periodic noises due to temperature variation. Random-stochastic noises have a well identified signature in time domain but periodic noises are difficult to analyze in time domain. However, in this paper, an effort is made to identify and analyze the deterministic trends of both random-stochastic noises and periodic noises due to variation in temperature using an alternate approach of least-squares normalized-error (LSNE) regression algorithm. A MATLAB based application with graphical user interface (GUI) is developed to estimate and analyze random-stochastic noises and periodic noises and re-estimate the stability of rubidium atomic clock after removing these noises from the raw phase data. The estimation of stationary noises are done using Allan variance from time domain data and noise profile is calculated using curve fit method. The estimation of periodic noises due to temperature variation is carried in frequency domain through spurious analysis of the frequency data of atomic clock.
Thesis Title:
Development of an Auto Impact Excitation Device for Operational Modal Testing (Control & Testing)
Supervisor: Dr. Ong Zhi Chao
Grade: A -
I was very grateful for my supervisor's guidance, seriously. He is one of the best lecturers I ever met in UM.
Sharing with you my dear readers who may find it useful.
Feel free to connect with me at maxermesilliam@gmail.com.
A Novel Displacement-amplifying Compliant Mechanism Implemented on a Modified...IJECEIAES
The micro-accelerometers are devices used to measure acceleration. They are implemented in applications such as tilt-control in spacecraft, inertial navigation, oil exploration, etc. These applications require high operating frequency and displacement sensitivity. But getting both high parameter values at the same time is difficult, because there are physical relationships, for each one, where the mass is involved. When the mass is reduced, the operating frequency is high, but the displacement sensitivity decreases and vice versa. The implementation of Displacement-amplifying Compliant Mechanism (DaCM) supports to this dependence decreases. In this paper the displacement sensitivity and operation frequency of a Conventional Capacitive Accelerometer are shown (CCA). A Capacitive Accelerometer with Extended Beams (CAEB) is also presented, which improves displacement sensitivity compared with CCA, and finally the implementation of DACM´s in the aforementioned devices was also carried out. All analyzed cases were developed considering the in-plane mode. The Matlab code used to calculate displacement sensitivity and operating frequency relationship is given in Appendix A.
Modeling and Estimation of Stationary and Non-stationary Noises of Rubidium A...IJERA Editor
Noise estimation of atomic clock is one of the important research areas in the field of atomic clock development and application. Most of the atomic clocks are having random-stochastic noises and periodic noises due to temperature variation. Random-stochastic noises have a well identified signature in time domain but periodic noises are difficult to analyze in time domain. However, in this paper, an effort is made to identify and analyze the deterministic trends of both random-stochastic noises and periodic noises due to variation in temperature using an alternate approach of least-squares normalized-error (LSNE) regression algorithm. A MATLAB based application with graphical user interface (GUI) is developed to estimate and analyze random-stochastic noises and periodic noises and re-estimate the stability of rubidium atomic clock after removing these noises from the raw phase data. The estimation of stationary noises are done using Allan variance from time domain data and noise profile is calculated using curve fit method. The estimation of periodic noises due to temperature variation is carried in frequency domain through spurious analysis of the frequency data of atomic clock.
The myphotonics project deals with the construction of opto-mechanical components and optical experiment implementation using modular systems such as LEGO®.
The components are low cost and the instructions that originated them are free to use. OpenAdaptonik and myphotonics can work together sharing the same purpose.
it is understanding about the undamped free vibration and its equation and function.........its very usefull for vibration system.......
its gives derivation of undamped free vibration.....
Design of Linear Array Transducer Using Ultrasound Simulation Program Field-IIinventy
This paper analyze the effect of number of elements of linear array and frequency influence the
image quality in a homogenous medium. Linear arrays are most common for conventional ultrasound imaging,
because of the advantages of electronic focusing and steering. Propagation of ultrasound in biological tissues is
of nonlinear in nature. But linear approximation in far-field is promising solution to model and simulate the
real time ultrasound wave propagation. The simulation of ultrasound imaging using linear acoustics has been
most widely used for understanding focusing, image formation and flow estimation, and it has become a
standard tool in ultrasound research. . In this paper the ultrasound field generated from linear array transducer
and propagation through biological tissues is modeled and simulated using FIELD II program.
Design of Vibration Test Fixture for Opto-Electronic EquipmentIJMERJOURNAL
ABSTRACT : In this paper an attempt is made in designing vibration test fixture for opto-electronic equipment. It can be achieved by formulating basic or preliminary 3D CAD assembled model followed by attaching material to its components. The analysis carried by defining the contact conditions of every part of it, defining the fixing conditions, applying loads virtually, good quality meshing, followed by optimization of the same by taking concurrence from the results of Linear Harmonic Structural Vibration Analysis. SolidworksSimulation premium software is used for modelling and solving the Linear Harmonic Structural vibration analysis for all Environmental Stress Screening (ESS) tests like vibration, shock for elimination of failures before physical testing. The comparison between experimental results and simulation results are presented in this paper.
The myphotonics project deals with the construction of opto-mechanical components and optical experiment implementation using modular systems such as LEGO®.
The components are low cost and the instructions that originated them are free to use. OpenAdaptonik and myphotonics can work together sharing the same purpose.
it is understanding about the undamped free vibration and its equation and function.........its very usefull for vibration system.......
its gives derivation of undamped free vibration.....
Design of Linear Array Transducer Using Ultrasound Simulation Program Field-IIinventy
This paper analyze the effect of number of elements of linear array and frequency influence the
image quality in a homogenous medium. Linear arrays are most common for conventional ultrasound imaging,
because of the advantages of electronic focusing and steering. Propagation of ultrasound in biological tissues is
of nonlinear in nature. But linear approximation in far-field is promising solution to model and simulate the
real time ultrasound wave propagation. The simulation of ultrasound imaging using linear acoustics has been
most widely used for understanding focusing, image formation and flow estimation, and it has become a
standard tool in ultrasound research. . In this paper the ultrasound field generated from linear array transducer
and propagation through biological tissues is modeled and simulated using FIELD II program.
Design of Vibration Test Fixture for Opto-Electronic EquipmentIJMERJOURNAL
ABSTRACT : In this paper an attempt is made in designing vibration test fixture for opto-electronic equipment. It can be achieved by formulating basic or preliminary 3D CAD assembled model followed by attaching material to its components. The analysis carried by defining the contact conditions of every part of it, defining the fixing conditions, applying loads virtually, good quality meshing, followed by optimization of the same by taking concurrence from the results of Linear Harmonic Structural Vibration Analysis. SolidworksSimulation premium software is used for modelling and solving the Linear Harmonic Structural vibration analysis for all Environmental Stress Screening (ESS) tests like vibration, shock for elimination of failures before physical testing. The comparison between experimental results and simulation results are presented in this paper.
Vibration Analysis and Modelling of a Cantilever Beam Muhammad Usman
This report in cooperates the techniques, adopted for the evaluation of vibration analysis of a cantilever beam using both techniques i.e. theoretical as well as the practical ones. Computer based analysis of a beam were also performed using Solid Works and Mat Lab software. These techniques helped a lot in finding the natural frequencies and in making the vibrational characteristic behavior of a cantilever beam thus steel used as a material.
MARKET ANALYSIS OF FINANCIAL INSTITUTIONS AND ENTREPRENEURSHIP IN INDIAIAEME Publication
The purpose of this research is to investigate early-stage ease/difficulties faced by
Start-Ups /MSME in India. The research is based in Bengaluru, Karnataka, India, five
major banks located in the city were approached. The amount of support offered by
banks to open a business bank account was investigated through interaction with
representatives
Evaluation of Vibrational Behavior for A System With TwoDegree-of-Freedom Und...IJERA Editor
Analysis of the vibrational behavior of a system is extremely important, both for the evaluation of operating conditions, as performance and safety reason. The studies on vibration concentrate their efforts on understanding the natural phenomena and the development of mathematical theories to describe the vibration of physical systems. The purpose of this study is to evaluate an undamped system with two-degrees-of-freedom and demonstrate by comparing the results obtained in the experimental, numerical and analytical modeling the characteristics that describe a structure in terms of its natural characteristics. The experiment was conducted in PUC-MG where the data were acquired to determine the natural frequency of the system. We also developed an experimental test bed for vibrations studies for graduate and undergraduate students. In analytical modeling were represented all the important aspects of the system. In order, to obtain the mathematical equations is used MATLAB to solve the equations that describe the characteristics of system behavior. For the simulation and numerical solution of the system, we use a computational tool ABAQUS. The comparison between the results obtained in the experiment and the numerical was considered satisfactory using the exact solutions. This study demonstrates that calculation of the adopted conditions on a system with two-degrees-of-freedom can be applied to complex systems with many degrees of freedom and proved to be an excellent learning tool for determining the modal analysis of a system. One of the goals is to use the developed platform to be used as a didactical experiment system for vibration and modal analysis classes at PUC Minas. The idea is to give the students an opportunity to test, play, calculate and confirm the results in vibration and modal analysis in a low-cost platform
Expert system design for elastic scattering neutrons optical model using bpnnijcsa
In present paper, a proposed expert system is designed to obtain a trained formulae for the optical model
parameters used in elastic scattering neutrons of light nuclei for (7Li), at energy range between [(1) to
(20)] MeV. A simple algorithm has used to design this expert system, while a multi-layer backwardpropagation
neural network (BPNN) is applied for training and testing the data used in this model. This
group of formulae may get a simple expert system occurring from governing formulae model, and predicts
the critical parameters usually resulted from the complicated computer coding methods. This expert system
may use in nuclear reactions yields in both fission and fusion nature who gives more closely results to the
real model.
Aeolian vibrations of overhead transmission line bundled conductors during in...Power System Operation
In part A of this paper, the frequency mobility response
of the excitation technique used to induce vibration on
a quad-bundled conductor rigidly attached indoors was
investigated. Two reference inputs were used to link
the shaker to the quad bundle conductors via a square
rigid block made of welded square hollow steel. The
primary objective was to determine whether there
was interference due to the use of a rigid connection.
In the first instance, restraining the free motion of the
bundle conductors which would be disadvantageous
to the vibration response results. The interference
was evaluated in the form of mobility FRF responses
Identification of coulomb, viscous and particle damping parameters from the r...ijiert bestjournal
This paper deals with Theoretical and Experimental methods for identification of coulomb ,Viscous and Particle
damping parameters from the response of Single degree of freedom harmonically forced linear oscillator when
system damped with more than one type of damping ,which parameter is responsible for the control of resonant
response of vibrating systems, in experimental method setup have been presented to investigate steady state
response amplitude xi for SDOF system for different values of amplitude Yi of the base excitation from this
relationship of (Xi ,Yi) the values of viscous damping coefficient „c‟ and coulomb friction force F0 ,also
equivalent viscous damping ratios ,have been calculated from frequency response analysis for the systems with
viscous damping ,Viscous and Coulomb friction damping, coulomb friction damping and particle damping by
using half power band-width method and in theoretical studies expression for steady state amplitude X0
obtained is used to study the effect of frequency ratio and coulomb friction parameters on phase angle and
amplitude ratio.
APPLICATION OF PARTICLE SWARM OPTIMIZATION TO MICROWAVE TAPERED MICROSTRIP LINEScseij
Application of metaheuristic algorithms has been of continued interest in the field of electrical engineering because of their powerful features. In this work special design is done for a tapered transmission line used for matching an arbitrary real load to a 50Ω line. The problem at hand is to match this arbitray load to 50 Ω line using three section tapered transmission line with impedances in decreasing order from the load. So the problem becomes optimizing an equation with three unknowns with various conditions. The optimized values are obtained using Particle Swarm Optimization. It can easily be shown that PSO is very strong in solving this kind of multiobjective optimization problems.
Application of particle swarm optimization to microwave tapered microstrip linescseij
Application of metaheuristic algorithms has been of continued interest in the field of electrical engineering
because of their powerful features. In this work special design is done for a tapered transmission line used
for matching an arbitrary real load to a 50Ω line. The problem at hand is to match this arbitray load to 50
Ω line using three section tapered transmission line with impedances in decreasing order from the load. So
the problem becomes optimizing an equation with three unknowns with various conditions. The optimized
values are obtained using Particle Swarm Optimization. It can easily be shown that PSO is very strong in
solving this kind of multiobjective optimization problems.
Application of Numerical and Experimental Simulations for the Vibrating Syste...IJERD Editor
In this work,there may be some requirements of finding out the coupling loss factors of system component.It becomes difficult to exactly know the coupling loss factor by looking at the behavior of the system. For this purpose, the numerical solution developed in this work. Initially, one need to extract the displacement, velocity and energy profiles of the system which has got the components installed for which the coupling loss factor need to be determined. Then the numerical simulations can be run for different coupling loss factor of the vibrating system and the coupling loss factor can be found when the simulation results match with the experimental measurements. In this paper the experimentation is carried out i for the model a)Pre-design application of the work developed. b) Post design application of the work developed. The numerical results converge very well towards the experimental results as the coupling loss factor in simulation is varied towards the actual value. Similarly, for the second approach the experimental results converge towards the simulation results of 0.15 as the coupling loss factor of the damper that is installed on the system is varied towards 0.15.
DAMPING INTER-AREA OSCILLATIONS IN POWER SYSTEMS USING A CDM-BASED PID CONTRO...Power System Operation
The interconnected energy transport system is the
mechanism that provides the stability of energy, or
the balance, between the centers of production and
consumption throughout the country. The
interconnected system adapts energy production to
changes in consumption. For many years, because of
long transmission lines or high-value power
transmission in weak-connected power systems, one
of the problems encountered is the existence of lowfrequency
oscillations between generator groups [1,
2]. These inter-area oscillations are a significant
issue in power system stability and control areas.
Modern power systems possess three main
properties: (1) the measure of interconnected system
is getting larger; (2) there is a closer operating point
to the power system stability limit because of
environmental and economic conditions; (3) being
composed of new elements and keeping pace with
technological developments unfortunately cause new
uncertainties in the stability of power systems. These
properties increase the risk of formation of lowfrequency
oscillations [3].
Centralized Optimal Control for a Multimachine Power System Stability Improve...IDES Editor
this paper introduces the application of wave variable
method in reducing the effect of delay during the transmission of
control signals via large distances in a multimachine power
system. Fast response and pure control signals applied to a power
system have great importance in control process. At first we
design a centralized optimal control considering no transport
delay and then we compare them to the one considering this effect
in order to demonstrate the deteriorating effect of transmission
delay. Then we apply the wave variable method and it is shown
that performance of centralized optimal controller is improved.
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Good quality Journals,
Research,
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Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
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IJETR, IJMCTR,
Journals,
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Monthly Journal,
Good quality Journals,
Research,
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Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
ER Publication,
IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
Research Papers,
Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
ER Publication,
IJETR, IJMCTR,
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International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
Research Papers,
Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
ER Publication,
IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
Research Papers,
Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
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IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
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Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
ER Publication,
IJETR, IJMCTR,
Journals,
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High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
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Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
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Monthly Journal,
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Engineering Journal,
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Monthly Journal,
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Engineering Journal,
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Journals,
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Monthly Journal,
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Research,
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Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
ER Publication,
IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
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Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
ER Publication,
IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
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Research,
Research Papers,
Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
ER Publication,
IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
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Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
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IJETR, IJMCTR,
Journals,
International Journals,
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Monthly Journal,
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Research,
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Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
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IJETR, IJMCTR,
Journals,
International Journals,
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Monthly Journal,
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Research,
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Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
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IJETR, IJMCTR,
Journals,
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Monthly Journal,
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Research,
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Research Article,
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Engineering Journal,
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Monthly Journal,
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Engineering Journal,
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Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
1. International Journal of Engineering and Technical Research (IJETR)
ISSN: 2321-0869, Volume-2, Issue-2, February 2014
60 www.erpublication.org
Abstract— The primary objective of vibration analysis is to
study response behavior of dynamic systems and excitation
forces associated with it. The technology of vibration testing has
rapidly evolved since World War II and the technique has been
successfully applied to a wide spectrum of products. Vibration
testing is usually performed by applying a vibratory excitation
to a test object and monitoring the structural integrity and
performance of the intended function of the object.
In this paper theoretical, experimental and numerical
analysis of SDoF system is carried out to find out damping
coefficient. The system identification is also carried out to
identify the various parameters of the system. e.g. ωn, m, k, ,
etc. of a single degree of freedom system.
Index Terms— Dynamic systems, Excitation, Monitoring,
Structural Integrity, Vibration Testing.
I. INTRODUCTION
Vibratory motion is repeated indefinitely and exchange of
energy takes place. The structures designed to support the
high speed engines and turbines are subjected to vibration.
Due to faulty design and poor manufacture there is unbalance
in the engines which causes excessive and unpleasant stresses
in the rotating system because of vibration. The vibration
causes rapid wear of machine parts such as bearings and
gears. Unwanted vibrations may cause loosening of parts
from the machine. Because of improper design or material
distribution, the wheels of locomotive can leave the track due
to excessive vibration which results in accident or heavy loss.
Many buildings, structures and bridges fall because of
vibration. If the frequency of excitation coincides with one of
the natural frequencies of the system, a condition of resonance
is reached, and dangerously large oscillations may occur
which result in mechanical failure of the system. Hence
vibration analysis is important in design field. The
single-degree-of-freedom (SDOF) system is the most widely
used and simplest model for vibration analysis. The SDOF
system is a simple but worthy model because it quantifies
many results of an isolation system [1].
A. Determination of Equivalent Viscous Damping from
Frequency Response Curve [2]:
Damping is a phenomenon by which mechanical energy is
dissipated, usually converted as a thermal energy in dynamic
systems [3].The damping in a system can be obtained from
Manuscript received Feb. 11, 2014.
Prof.Dr.S.H.Sawant, Associate Professor, Mechanical Engg.Dept, Dr.J.
J. Magdum college of Engineering, Jaysingpur, Kolhapur, India
free vibration decay curve where the free vibration test is not
practical. The damping may be obtained from the frequency
response curve of forced vibration test.
The frequency – response curve as obtained for a system
excited with a constant force, as shown in Fig. 1.1
Fig. 1.1 Determination of Equivalent Viscous Damping
from Frequency Response Curve
The magnification at resonance is given by ½ . It is difficult,
however to get the exact resonance point since the peak point
occurs slightly away from the resonance. If the amplitude of
vibration and the magnification can be found out at resonance
then the damping factor is given by –
=
resFM .).(2
1
The fact that the phase difference between the exciting force
and displacement is 900
at resonance is made to use in locating
the resonant point. The phase difference () between the force
and the displacement is given by
Y
X1
sin
To determine the damping in a system if you have
just frequency response curve of the system with constant
excitation, damping in the system is determined by assuming
the damping is of viscous nature.
As we know that,
2
1
st
P
X
X
(1.1)
By drawing a horizontal line at X = 0.707 Xp, cutting the
response curve at two points the corresponding value of
abscissa being 1 and ω2.
The magnification factor is given by equation,
Design and Development of Experimental setup for
Identification of SDoF with Harmonic Excitation
Prof. Dr. S. H. Sawant
2. Design and Development of Experimental setup for Identification of SDoF with Harmonic Excitation
61 www.erpublication.org
stX
X
222
21
1
nn
For point A and B then equation can be written as,
st
p
X
X707.0
222
21
1
nn
(1.2)
In above equation ωp has been written in place of ωn
because it is taken that ωn = ωp as a first approximation. Also
the values of ω in the equation corresponding to ω1 and ω2.
From equation (1.1) an d (1.2),
2
707.0 p
X
222
21
1
nn
Finally we have,
2
2
12
(1.3)
Fig 1.2 Determination of Equivalent Viscous Damping
from Frequency Response Curve
Or 2
OP
AB
OP
AB
2
1
(1.4)
Taking these measurement from the frequency
response curve after making necessary construction, we get
the first approximate value of .
To get an accurate value of , use as obtained
above to determine the nature frequency of the system from
equation,
2
21
n
p
ωn =
2
21
p
(1.5)
Mark this point as N on the abscissa and draw an ordinate
as shown in Fig.1.2 . The height of this ordinate upto the curve
gives the resonance amplitude xr.
Now repeat the process by first drawing a horizontal line at
a height X = 0.707 Xr and then finding the frequencies ω1 and
ω2 corresponding to the point of intersection. Then in a
similar manner it can be shown that –
n
12
2
(1.6)
Hence an accurate value of can be found by construction
and measurements.
B. System Identification from Frequency Response:
System identification means to identify the various
parameters of the system. e.g. ωn, m, k, , etc. of a system.
In order to do this, a known constant force Fo at a variable
frequency is applied to the system and the frequency response
curve similar to the Fig. 1.2.is obtained.
Different parameters can be obtained as follows,
I. Obtain ωn and as per equation,
ωn =
2
21
p
, and
n
12
2
II. The magnification at resonance (ω = ωn) can
be obtained as,
2
1
st
P
X
X
Where Xr is the resonant
amplitude
2
1
0
K
F
Xr
K =
r
o
X
F
2
III. The natural frequency ωn having been
obtained at step I above and k at step II
ωn =
m
K
thus the mass is
obtained as
m = 2
n
K
IV. Similarly the damping coefficient c can be
obtained as,
C = Km2
3. International Journal of Engineering and Technical Research (IJETR)
ISSN: 2321-0869, Volume-2, Issue-2, February 2014
62 www.erpublication.org
II. DESIGN AND EXPERIMENTATION
A. Conceptual Design
After studying the problem thoroughly different possible
solutions came up out of that most practical and cost effective
experimental setup were developed [4] as shown in Fig.2.1.
For excitation electric motor and the cam and follower
mechanism is used. The cam is coupled with the motor and
motor is connected to the dimmer-stat. Helical spring is used
in order to include the freedom. There are various devices
which are used to measure the vibration level in the system.
Fig.2.1 Experimental setup for Analysis of SDOF
Vibration
Following are the experimental results found out during
experiment for analysis of SDoF vibrations.
Table 2.1.Magnification Factor and Frequency Ratio
Χ(mm) Ư(mm) ω(rad/sec) ωn(rad/sec) Χ/Ư ω/ωn
4 4 18.485 73.94 1 0.25
5 4 36.97 73.94 1.25 0.50
7 4 68.29 73.94 1.75 0.92
3 4 92.425 73.94 0.75 1.25
2.5 4 110.91 73.94 0.625 1.5
The graph of magnification factor vs. frequency ratio is
plotted as shown in Fig.2.2
/n
Fig 2.2 Graph between Magnification Factor vs.
Frequency Ratio for Experimental Results
III. THEORETICAL ANALYSIS
For Theoretical Analysis consider the system excited by
support as shown in Fig.3.1, According to support excitation
theory,
Fig. 3.1 Support Excitation
222
2
21
21
U
X
(3.1)
Where,
n
Values of magnification factor are established out for various
frequency ratios.
( ) 0.25 0.5 0.89 1.25 1.5
X/U 1.065 1.289 1.934 1.192 0.876
Graph is plotted as shown in Fig.3.2 for various values of
magnification factor which are found out for various
frequency ratios.
/n
Fig.3.2 Graph between Magnification Factor vs.
Frequency Ratio for Theoretical Results.
IV. NUMERICAL ANALYSIS
For numerical analysis MATLAB software is used to validate
of the experimental and theoretical results. MATLAB
program is developed to find out various values of
magnification factor for various frequency ratios. Equation
3.1 is modeled in MATLAB to obtain the following results.
( ) 02 0.4 1 1.2 1.4
X/U 1.041 1.176 1.894 1.441 1.023
Graph is plotted as shown in Fig.3.3 for various values of
magnification factor which are found out for various
frequency ratios.
Parameter
K
(N/m) (rad/sec)
C
(N-sec/m)
Value 4291 73.94 64.38
X/U
X/U
4. Design and Development of Experimental setup for Identification of SDoF with Harmonic Excitation
63 www.erpublication.org
Fig 4.3 Graph between Magnification Factor vs.
Frequency Ratio for Numerical Results
Fig 4.4 Magnification Factor vs. Frequency Ratio for
Theoretical, Experimental and Numerical Results
Now, from theoretical results the various parameters of the
system.e.g. ωn, m, k, , etc. of system were determined as
follows
Parameter
K
(N/m) (rad/sec)
C(N-sec/m)
Value 4291 73.94 70.52
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V. CONCLUSION
In this paper analysis of SDoF system is carried
theoretically, experimentally and numerically to find out
damping coefficient. System identification is also carried out
to identify the various parameters of the system. e.g. ωn, m, k,
, etc. of a SDoF system. It is found out that there is slight
variation in experimental, theoretical and numerical values
which are may be due to errors such as measuring or
computational errors.
ACKNOWLEDGMENT
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American English is without an ―e‖ after the ―g.‖ Use the
singular heading even if you have many acknowledgments.
Avoid expressions such as ―One of us (S.B.A.) would like to
thank ... .‖ Instead, write ―F. A. Author thanks ... .‖ Sponsor
and financial support acknowledgments are placed in the
unnumbered footnote on the first page.
REFERENCES
[1] Dino Sciulli, ―Dynamics and Control for Vibration Isolation
Design‖, Dissertation submitted to the Faculty of the Virginia
Polytechnic Institute and State University.
[2] S. S. Rao, ―Mechanical Vibrations‖, 3rd
ed. Addison-Wesley
Publishing Company (1995).
[3] A.S.N.Saiteja, C.H.Pavan Kumar, ―Determining Hysteresis
Damping in a Steam Turbine Blade using a Finite Element Tool‖,
International Journal of Innovative Technology and Exploring
Engineering (IJITEE) ISSN: 2278-3075, Volume-2, Issue-2,
January 2013.
[4] C. Walshaw, ―Mechanical Vibration with Applications‖, Ellis
Horwood Limited, New York.
Prof.S.H.Sawant is working as Associate Professor
in Mechanical Engineering Department, Co-ordinator
of M.E. Mechanical (Machine Design) Program and
Dean, Faculty Development Cell of Dr.J.J.Magdum
College of Engineering, Jaysingpur, Dist. Kolhapur,
Maharashtra State. He has been awarded as the Best
Teacher by the Institute. He is Life Member of IOE,
TSI, ISTE and Member of SAE. He has number of
Publications in National and International
Conferences and Journals. He has Provided Consultancy to Various
Industries and Research Centres. He has awarded with Best Paper Award in
International Conference at Pattaya, Thailand. He worked as Organizing
Secretary of International Conference on Emerging Trends in Engineering
(ICETE 2013).He has submitted his Ph.D. Thesis at Shivaji University,
Kolhapur in Mechanical Engineering.