FREE VIBRATION WITH COULOMB DAMPING Revision A
|
|
- Iris Hood
- 5 years ago
- Views:
Transcription
1 By Tom Irvine June 5, 010 FREE VIBRATION WITH COULOMB DAMPING Revision A g m F sgn () & Figure 1. Coulomb damping is dry friction damping. Consider the free vibration response of a singledegree-of-freedom system subjected to Coulomb damping. The damping force F is where F = µ mg (1) µ = friction coefficient m = mass g = acceleration of gravity Assume that the friction coefficient is constant for simplicity. 1
2 Force +F 0 Velocity -F Figure. Coulomb Force vs. Velocity The governing equation of motion for the displacement is m & + = Fsgn () & () where = stiffness The sgn (& ) function represents the sign of &. As an alternative, the governing equation can be written as & m& + = F (3) & The governing equation is solved in a piecewise-linear manner.
3 Assume that initial displacement (0) is (0) > F / (4) Also assume that the initial velocity is zero. Consider the equation of motion for negative velocity. m & + = F for & < 0 (5) F & & + = (6) m m The natural frequency n is n = (7) m Let F E = (8) m & + n = E (9) The equation is solved using Laplace transforms. L { & + n } = L{ E} & (10) E s X(s) s (0) + n X(s) = (11) s 3
4 E [ s n ] X(s) s (0) = s + (1) E [ s n ] X(s) = + s (0) + (13) s E s (0) X(s) = (14) s + [ s + ] [ n s + n ] Tae the inverse Laplace transform. (t) E = (0) cos nt + [ 1 cos nt] (15) n (t) E E = + (0) cos nt (16) n n (t) F F = + (0) cos nt (17) m m n n (t) F F = + (0) cos nt for & < 0 (18) F & (t) = n (0) sin nt for sin n t > 0 (19) The velocity equals zero at t = π / n (0) 4
5 The displacement at this time is π = n F F + (0) + (1) = n π F (0) () Consider the equation of motion for positive velocity. m& + = F for & > 0 (3) The initial displacement term must be reset to the last displacement for negative velocity. Furthermore, a phase angle must be added to the argument in the cosine term. F F F ( t) = + (0) + cos( n t + π) for & > 0 (4) F 3F ( t) = + (0) cos( nt + π) for & > 0 (5) 3F & ( t) = n (0) sin( nt + π) (6) The first negative displacement pea thus has an amplitude that is F/ less than the initial displacement in terms of absolute values. This reduction factor can also be derived from the wor-energy relationship in Appi A. The pattern continues such that the envelope has a linear decay. 5
6 The velocity returns to zero for t = π / n (7) π = n F 3F (0) (8) π = (0) n 4F (9) Each consecutive positive pea is thus 4 F/ lower than the previous positive pea. The process is then repeated. Eample A single-degree-of-freedom system has mass = 1 g stiffness = 0,000 N/m friction coefficient = 0.4 initial displacement = 5 mm The resulting displacement is shown in Figure 3. The displacement converges to F /, where F = µ mg. Deping on the initial displacement, the displacement may also converge to F /. 6
7 SDOF RESPONSE DRY FRICTION fn=.51 Hz DISPLACEMENT (mm) TIME (SEC) Figure 3. References 1. R. Vierc, Vibration Analysis, nd Edition, Harper Collins, New Yor, W. Thomson, Theory of Vibration with Applications nd Edition, Prentice Hall, New Jersey,
8 APPENDIX A Energy Method The potential energy is set equal to the wor done by friction for one cycle. 1 ( ) = F( + ) 1 1 (A-1) where 1 and are consecutive positive peas. Note that the inetic energy is zero at the instantaneous time that each pea occurs. The wor-energy relationship is satisfied if 1 F = ( 1 ) (A-) F 1 = (A-3) ( ) 8
9 APPENDIX B Matlab Script disp(' '); disp(' dry.m ver 1.0 June 5, 005 '); disp(' by Tom Irvine tomirvine@aol.com '); disp(' '); disp(' This program calculates the response of a '); disp(' single-degree-of-freedom system subjected to dry damping '); disp(' '); clear all; disp(' Enter mass (g) ') m=input(' '); disp(' Enter stiffness (N/m) ') =input(' '); disp(' Enter coefficient of friction ') mu=input(' '); disp(' Enter initial displacement (mm) ') o=input(' '); o=o/1000.; F=mu*m*(9.81); f=f/; omegan=sqrt(/m); fn=omegan/(.*pi); out1=sprintf('\n fn = 8.4g Hz\n',fn); disp(out1); out1=sprintf(' F/ = 8.4g mm\n',(f/)*1000.); disp(out1); if( F/ > o ) disp(' '); disp(' No oscillation. '); disp(' F/ > o '); T=1/fn; dt = T/100.; delta=.*pi/100; num=1.*t/dt; j=1; 9
10 10 tdelay=0.; arg=0.; for(i=1:(num+1)) t(i)=(i-1)*dt; arg=arg+delta; if(arg>.*pi) arg=arg-.*pi; if(arg>=0 && arg<=pi) if( (o-f) <=0) (i)=o; else (i)= f +( o - f )*cos(arg); 1=(i); else if( abs(1) < f ) (i)=1; else (i)= -f +( 1 + f )*cos(arg+pi); o=(i); =*1000.; plot(t,); label(' Time(sec) '); ylabel(' Displacement(mm) '); out1=sprintf(' SDOF Response Dry Friction fn=8.4g Hz ',fn); title(out1); grid on; 10
Direct Fatigue Damage Spectrum Calculation for a Shock Response Spectrum
Direct Fatigue Damage Spectrum Calculation for a Shock Response Spectrum By Tom Irvine Email: tom@vibrationdata.com June 25, 2014 Introduction A fatigue damage spectrum (FDS) was calculated for a number
More informationSHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 1B. Damping
SHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 1B. Damping By Tom Irvine Introduction Recall the homework assignment from Unit 1A. The data.txt time history represented a rocket vehicle dropped from
More informationEQUIVALENT STATIC LOADS FOR RANDOM VIBRATION Revision B
EQUIVALENT STATIC LOADS FOR RANDOM VIBRATION Revision B By Tom Irvine February 20, 2001 Email: tomirvine@aol.com Introduction A particular engineering design problem is to determine the equivalent static
More informationEFFECTIVE MODAL MASS & MODAL PARTICIPATION FACTORS Revision F
EFFECTIVE MODA MASS & MODA PARTICIPATION FACTORS Revision F By Tom Irvine Email: tomirvine@aol.com March 9, 1 Introduction The effective modal mass provides a method for judging the significance of a vibration
More informationSHOCK RESPONSE OF MULTI-DEGREE-OF-FREEDOM SYSTEMS Revision F By Tom Irvine May 24, 2010
SHOCK RESPONSE OF MULTI-DEGREE-OF-FREEDOM SYSTEMS Revision F By Tom Irvine Email: tomirvine@aol.com May 4, 010 Introduction The primary purpose of this tutorial is to present the Modal Transient method
More informationTWO-STAGE ISOLATION FOR HARMONIC BASE EXCITATION Revision A. By Tom Irvine February 25, 2008
TWO-STAGE ISOLATION FOR HARMONIC BASE EXCITATION Revision A By Tom Irvine Email: tomirvine@aol.com February 5, 008 Introduction Consider a base plate mass m and an avionics mass m modeled as two-degree-of-freedom.
More informationOptimized PSD Envelope for Nonstationary Vibration Revision A
ACCEL (G) Optimized PSD Envelope for Nonstationary Vibration Revision A By Tom Irvine Email: tom@vibrationdata.com July, 014 10 FLIGHT ACCELEROMETER DATA - SUBORBITAL LAUNCH VEHICLE 5 0-5 -10-5 0 5 10
More informationSHOCK RESPONSE SPECTRUM ANALYSIS VIA THE FINITE ELEMENT METHOD Revision C
SHOCK RESPONSE SPECTRUM ANALYSIS VIA THE FINITE ELEMENT METHOD Revision C By Tom Irvine Email: tomirvine@aol.com November 19, 2010 Introduction This report gives a method for determining the response of
More informationIntroduction to Vibration. Professor Mike Brennan
Introduction to Vibration Professor Mie Brennan Introduction to Vibration Nature of vibration of mechanical systems Free and forced vibrations Frequency response functions Fundamentals For free vibration
More informationEach of these functions represents a signal in terms of its spectral components in the frequency domain.
N INTRODUCTION TO SPECTRL FUNCTIONS Revision B By Tom Irvine Email: tomirvine@aol.com March 3, 000 INTRODUCTION This tutorial presents the Fourier transform. It also discusses the power spectral density
More informationMECHANICS LAB AM 317 EXP 8 FREE VIBRATION OF COUPLED PENDULUMS
MECHANICS LAB AM 37 EXP 8 FREE VIBRATIN F CUPLED PENDULUMS I. BJECTIVES I. To observe the normal modes of oscillation of a two degree-of-freedom system. I. To determine the natural frequencies and mode
More informationSHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 29. Shock Response Spectrum Synthesis via Wavelets
SHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 29. Shock Response Spectrum Synthesis via Wavelets By Tom Irvine Email: tomirvine@aol.com Introduction Mechanical shock can cause electronic components
More informationMathematical Modeling and response analysis of mechanical systems are the subjects of this chapter.
Chapter 3 Mechanical Systems A. Bazoune 3.1 INRODUCION Mathematical Modeling and response analysis of mechanical systems are the subjects of this chapter. 3. MECHANICAL ELEMENS Any mechanical system consists
More informationLecture XXVI. Morris Swartz Dept. of Physics and Astronomy Johns Hopkins University November 5, 2003
Lecture XXVI Morris Swartz Dept. of Physics and Astronomy Johns Hopins University morris@jhu.edu November 5, 2003 Lecture XXVI: Oscillations Oscillations are periodic motions. There are many examples of
More informationSecond-Order Linear Differential Equations C 2
C8 APPENDIX C Additional Topics in Differential Equations APPENDIX C. Second-Order Homogeneous Linear Equations Second-Order Linear Differential Equations Higher-Order Linear Differential Equations Application
More informationME scope Application Note 28
App Note 8 www.vibetech.com 3/7/17 ME scope Application Note 8 Mathematics of a Mass-Spring-Damper System INTRODUCTION In this note, the capabilities of ME scope will be used to build a model of the mass-spring-damper
More informationIntroduction to structural dynamics
Introduction to structural dynamics p n m n u n p n-1 p 3... m n-1 m 3... u n-1 u 3 k 1 c 1 u 1 u 2 k 2 m p 1 1 c 2 m2 p 2 k n c n m n u n p n m 2 p 2 u 2 m 1 p 1 u 1 Static vs dynamic analysis Static
More information1-DOF Vibration Characteristics. MCE371: Vibrations. Prof. Richter. Department of Mechanical Engineering. Handout 7 Fall 2017
MCE371: Vibrations Prof. Richter Department of Mechanical Engineering Handout 7 Fall 2017 Free Undamped Vibration Follow Palm, Sect. 3.2, 3.3 (pp 120-138), 3.5 (pp 144-151), 3.8 (pp. 167-169) The equation
More informationStructural Dynamics. Spring mass system. The spring force is given by and F(t) is the driving force. Start by applying Newton s second law (F=ma).
Structural Dynamics Spring mass system. The spring force is given by and F(t) is the driving force. Start by applying Newton s second law (F=ma). We will now look at free vibrations. Considering the free
More informationChapter 13. F =!kx. Vibrations and Waves. ! = 2" f = 2" T. Hooke s Law Reviewed. Sinusoidal Oscillation Graphing x vs. t. Phases.
Chapter 13 Vibrations and Waves Hooke s Law Reviewed F =!k When is positive, F is negative ; When at equilibrium (=0, F = 0 ; When is negative, F is positive ; 1 2 Sinusoidal Oscillation Graphing vs. t
More informationSTRUCTURAL DYNAMICS BASICS:
BASICS: STRUCTURAL DYNAMICS Real-life structures are subjected to loads which vary with time Except self weight of the structure, all other loads vary with time In many cases, this variation of the load
More informationExtending Steinberg s Fatigue Analysis of Electronics Equipment Methodology to a Full Relative Displacement vs. Cycles Curve
Extending Steinberg s Fatigue Analysis of Electronics Equipment Methodology to a Full Relative Displacement vs. Cycles Curve Revision C By Tom Irvine Email: tom@vibrationdata.com March 13, 2013 Vibration
More informationMODELLING A MASS / SPRING SYSTEM Free oscillations, Damping, Force oscillations (impulsive and sinusoidal)
DOING PHYSICS WITH MATLAB MODELLING A MASS / SPRING SYSTEM Free oscillations, Damping, Force oscillations (impulsive and sinusoidal) Download Directory: Matlab mscripts osc_harmonic01.m The script uses
More informationDynamics of structures
Dynamics of structures 2.Vibrations: single degree of freedom system Arnaud Deraemaeker (aderaema@ulb.ac.be) 1 Outline of the chapter *One degree of freedom systems in real life Hypothesis Examples *Response
More informatione jωt = cos(ωt) + jsin(ωt),
This chapter introduces you to the most useful mechanical oscillator model, a mass-spring system with a single degree of freedom. Basic understanding of this system is the gateway to the understanding
More informationME 563 HOMEWORK # 7 SOLUTIONS Fall 2010
ME 563 HOMEWORK # 7 SOLUTIONS Fall 2010 PROBLEM 1: Given the mass matrix and two undamped natural frequencies for a general two degree-of-freedom system with a symmetric stiffness matrix, find the stiffness
More informationThe student will experimentally determine the parameters to represent the behavior of a damped oscillatory system of one degree of freedom.
Practice 3 NAME STUDENT ID LAB GROUP PROFESSOR INSTRUCTOR Vibrations of systems of one degree of freedom with damping QUIZ 10% PARTICIPATION & PRESENTATION 5% INVESTIGATION 10% DESIGN PROBLEM 15% CALCULATIONS
More informationModeling and Experimentation: Mass-Spring-Damper System Dynamics
Modeling and Experimentation: Mass-Spring-Damper System Dynamics Prof. R.G. Longoria Department of Mechanical Engineering The University of Texas at Austin July 20, 2014 Overview 1 This lab is meant to
More informationLecture 25: Tue Nov 27, 2018
Lecture 25: Tue Nov 27, 2018 Reminder: Lab 3 moved to Tuesday Dec 4 Lecture: review time-domain characteristics of 2nd-order systems intro to control: feedback open-loop vs closed-loop control intro to
More informationOscillations. Phys101 Lectures 28, 29. Key points: Simple Harmonic Motion (SHM) SHM Related to Uniform Circular Motion The Simple Pendulum
Phys101 Lectures 8, 9 Oscillations Key points: Simple Harmonic Motion (SHM) SHM Related to Uniform Circular Motion The Simple Pendulum Ref: 11-1,,3,4. Page 1 Oscillations of a Spring If an object oscillates
More informationCHAPTER 6 STATE SPACE: FREQUENCY RESPONSE, TIME DOMAIN
CHAPTER 6 STATE SPACE: FREQUENCY RESPONSE, TIME DOMAIN 6. Introduction Frequency Response This chapter will begin with the state space form of the equations of motion. We will use Laplace transforms to
More informationGeotechnical Earthquake Engineering
Geotechnical Earthquake Engineering by Dr. Deepankar Choudhury Professor Department of Civil Engineering IIT Bombay, Powai, Mumbai 400 076, India. Email: dc@civil.iitb.ac.in URL: http://www.civil.iitb.ac.in/~dc/
More informationStep 1: Mathematical Modeling
083 Mechanical Vibrations Lesson Vibration Analysis Procedure The analysis of a vibrating system usually involves four steps: mathematical modeling derivation of the governing uations solution of the uations
More informationOptimized PSD Envelope for Nonstationary Vibration
Optimized PSD Envelope for Nonstationary Vibration Tom Irvine Dynamic Concepts, Inc NASA Engineering & Safety Center (NESC) 3-5 June 2014 The Aerospace Corporation 2010 The Aerospace Corporation 2012 Vibrationdata
More informationSHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 7A. Power Spectral Density Function
SHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 7A. Power Spectral Density Function By Tom Irvine Introduction A Fourier transform by itself is a poor format for representing random vibration because
More informationSome Aspects of Structural Dynamics
Appendix B Some Aspects of Structural Dynamics This Appendix deals with some aspects of the dynamic behavior of SDOF and MDOF. It starts with the formulation of the equation of motion of SDOF systems.
More informationSingle-Degree-of-Freedom (SDOF) and Response Spectrum
Single-Degree-of-Freedom (SDOF) and Response Spectrum Ahmed Elgamal 1 Dynamics of a Simple Structure The Single-Degree-Of-Freedom (SDOF) Equation References Dynamics of Structures, Anil K. Chopra, Prentice
More informationSimple Harmonic Motion of Spring
Nae P Physics Date iple Haronic Motion and prings Hooean pring W x U ( x iple Haronic Motion of pring. What are the two criteria for siple haronic otion? - Only restoring forces cause siple haronic otion.
More informationOscillations. Simple Harmonic Motion (SHM) Position, Velocity, Acceleration SHM Forces SHM Energy Period of oscillation Damping and Resonance
Oscillations Simple Harmonic Motion (SHM) Position, Velocity, Acceleration SHM Forces SHM Energy Period of oscillation Damping and Resonance 1 Revision problem Please try problem #31 on page 480 A pendulum
More informationProb. 1 SDOF Structure subjected to Ground Shaking
Prob. 1 SDOF Structure subjected to Ground Shaking What is the maximum relative displacement and the amplitude of the total displacement of a SDOF structure subjected to ground shaking? magnitude of ground
More informationVibrations in Free and Forced Single Degree of Freedom (SDOF) Systems
Vibrations in Free and Forced Single Degree of Freedom (SDOF) Systems Sneha Gulab Mane B.Tech (Mechanical Engineering), Department of Mechanical Engineering, Anurag Group of Institutions, Hyderabad, India.
More informationCh 3.7: Mechanical & Electrical Vibrations
Ch 3.7: Mechanical & Electrical Vibrations Two important areas of application for second order linear equations with constant coefficients are in modeling mechanical and electrical oscillations. We will
More informationVTU-NPTEL-NMEICT Project
MODULE-II --- SINGLE DOF FREE S VTU-NPTEL-NMEICT Project Progress Report The Project on Development of Remaining Three Quadrants to NPTEL Phase-I under grant in aid NMEICT, MHRD, New Delhi SME Name : Course
More informationTOPIC E: OSCILLATIONS SPRING 2019
TOPIC E: OSCILLATIONS SPRING 2019 1. Introduction 1.1 Overview 1.2 Degrees of freedom 1.3 Simple harmonic motion 2. Undamped free oscillation 2.1 Generalised mass-spring system: simple harmonic motion
More informationOutline of parts 1 and 2
to Harmonic Loading http://intranet.dica.polimi.it/people/boffi-giacomo Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano March, 6 Outline of parts and of an Oscillator
More informationVibrations of a mechanical system with inertial and forced disturbance
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 78-1684,p-ISSN: 3-334X, Volume 1, Issue 6 Ver. VI (Nov. - Dec. 15), PP 1-5 www.iosrjournals.org Vibrations of a mechanical system with
More informationChapter 4. Oscillatory Motion. 4.1 The Important Stuff Simple Harmonic Motion
Chapter 4 Oscillatory Motion 4.1 The Important Stuff 4.1.1 Simple Harmonic Motion In this chapter we consider systems which have a motion which repeats itself in time, that is, it is periodic. In particular
More informationSHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 6A. The Fourier Transform. By Tom Irvine
SHOCK ND VIBRTION RESPONSE SPECTR COURSE Unit 6. The Fourier Transform By Tom Irvine Introduction Stationary vibration signals can be placed along a continuum in terms of the their qualitative characteristics.
More informationSHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 6B. Notes on the Fourier Transform Magnitude
SHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 6B. Notes on the Fourier Transform Magnitude By Tom Irvine Introduction Fourier transforms, which were introduced in Unit 6A, have a number of potential
More informationPeriodic Motion. Periodic motion is motion of an object that. regularly repeats
Periodic Motion Periodic motion is motion of an object that regularly repeats The object returns to a given position after a fixed time interval A special kind of periodic motion occurs in mechanical systems
More informationDate: _15 April (1) The only reference material you may use is one 8½x11 crib sheet and a calculator.
PH1140: Oscillations and Waves Name: SOLUTIONS Conference: Date: _15 April 2005 EXAM #2: D2005 INSTRUCTIONS: (1) The only reference material you may use is one 8½x11 crib sheet and a calculator. (2) Show
More informationModeling and Experimentation: Compound Pendulum
Modeling and Experimentation: Compound Pendulum Prof. R.G. Longoria Department of Mechanical Engineering The University of Texas at Austin Fall 2014 Overview This lab focuses on developing a mathematical
More information7. FORCE ANALYSIS. Fundamentals F C
ME 352 ORE NLYSIS 7. ORE NLYSIS his chapter discusses some of the methodologies used to perform force analysis on mechanisms. he chapter begins with a review of some fundamentals of force analysis using
More informationEngineering Science OUTCOME 2 - TUTORIAL 3 FREE VIBRATIONS
Unit 2: Unit code: QCF Level: 4 Credit value: 5 Engineering Science L/60/404 OUTCOME 2 - TUTORIAL 3 FREE VIBRATIONS UNIT CONTENT OUTCOME 2 Be able to determine the behavioural characteristics of elements
More informationIntroduction Course Goals Review Topics. MCE371: Vibrations. Prof. Richter. Department of Mechanical Engineering. Handout 1 Fall 2017
MCE371: Vibrations Prof. Richter Department of Mechanical Engineering Handout 1 Fall 2017 Outline Introduction 1 Introduction Vibration Problems in Engineering 2 3 Vibration Problems in Engineering Vibration
More informationChapter 1. Harmonic Oscillator. 1.1 Energy Analysis
Chapter 1 Harmonic Oscillator Figure 1.1 illustrates the prototypical harmonic oscillator, the mass-spring system. A mass is attached to one end of a spring. The other end of the spring is attached to
More informationInput-Output Peak Picking Modal Identification & Output only Modal Identification and Damage Detection of Structures using
Input-Output Peak Picking Modal Identification & Output only Modal Identification and Damage Detection of Structures using Time Frequency and Wavelet Techniquesc Satish Nagarajaiah Professor of Civil and
More informationVibrations Qualifying Exam Study Material
Vibrations Qualifying Exam Study Material The candidate is expected to have a thorough understanding of engineering vibrations topics. These topics are listed below for clarification. Not all instructors
More informationFaculty of Computers and Information. Basic Science Department
18--018 FCI 1 Faculty of Computers and Information Basic Science Department 017-018 Prof. Nabila.M.Hassan 18--018 FCI Aims of Course: The graduates have to know the nature of vibration wave motions with
More informationCMPT 889: Lecture 2 Sinusoids, Complex Exponentials, Spectrum Representation
CMPT 889: Lecture 2 Sinusoids, Complex Exponentials, Spectrum Representation Tamara Smyth, tamaras@cs.sfu.ca School of Computing Science, Simon Fraser University September 26, 2005 1 Sinusoids Sinusoids
More informationIn-Structure Response Spectra Development Using Complex Frequency Analysis Method
Transactions, SMiRT-22 In-Structure Response Spectra Development Using Complex Frequency Analysis Method Hadi Razavi 1,2, Ram Srinivasan 1 1 AREVA, Inc., Civil and Layout Department, Mountain View, CA
More informationExamination paper for TMA4195 Mathematical Modeling
Department of Mathematical Sciences Examination paper for TMA4195 Mathematical Modeling Academic contact during examination: Elena Celledoni Phone: 48238584, 73593541 Examination date: 11th of December
More informationCFD DESIGN OF A GENERIC CONTROLLER FOR VORTEX-INDUCED RESONANCE
Seventh International Conference on CFD in the Minerals and Process Industries CSIRO, Melbourne, Australia 9-11 December 2009 CFD DESIGN OF A GENERIC CONTROLLER FOR VORTEX-INDUCED RESONANCE Andrew A. ANTIOHOS,
More informationPHYSICS. Chapter 15 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 15 Lecture RANDALL D. KNIGHT Chapter 15 Oscillations IN THIS CHAPTER, you will learn about systems that oscillate in simple harmonic
More informationChapter 14 Oscillations
Chapter 14 Oscillations Chapter Goal: To understand systems that oscillate with simple harmonic motion. Slide 14-2 Chapter 14 Preview Slide 14-3 Chapter 14 Preview Slide 14-4 Chapter 14 Preview Slide 14-5
More informationOverview of motors and motion control
Overview of motors and motion control. Elements of a motion-control system Power upply High-level controller ow-level controller Driver Motor. Types of motors discussed here; Brushed, PM DC Motors Cheap,
More informationسایت آموزش مهندسی مکانیک
http://www.drshokuhi.com سایت آموزش مهندسی مکانیک 1 Single-degree-of-freedom Systems 1.1 INTRODUCTION In this chapter the vibration of a single-degree-of-freedom system will be analyzed and reviewed. Analysis,
More informationMAT 275 Laboratory 4 MATLAB solvers for First-Order IVP
MAT 275 Laboratory 4 MATLAB solvers for First-Order IVP In this laboratory session we will learn how to. Use MATLAB solvers for solving scalar IVP 2. Use MATLAB solvers for solving higher order ODEs and
More informationVibration Isolation Control of Inertial navigation sensors Using Transfer Matrix Method for Multibody Systems
16 th International Conference on AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT - 16 May 26-28, 215, E-Mail: asat@mtc.edu.eg Military Technical College, Kobry Elkobbah, Cairo, Egypt Tel : +(22) 2425292
More information1.1 To observe the normal modes of oscillation of a two degree of freedom system.
I. BJECTIVES. To observe the normal modes of oscillation of a two degree of freedom system.. To determine the natural frequencies and mode shapes of the system from solution of the Eigenvalue problem..3
More information4.9 Free Mechanical Vibrations
4.9 Free Mechanical Vibrations Spring-Mass Oscillator When the spring is not stretched and the mass m is at rest, the system is at equilibrium. Forces Acting in the System When the mass m is displaced
More informationME8230 Nonlinear Dynamics
ME8230 Nonlinear Dynamics Lecture 1, part 1 Introduction, some basic math background, and some random examples Prof. Manoj Srinivasan Mechanical and Aerospace Engineering srinivasan.88@osu.edu Spring mass
More informationLecture 9: Eigenvalues and Eigenvectors in Classical Mechanics (See Section 3.12 in Boas)
Lecture 9: Eigenvalues and Eigenvectors in Classical Mechanics (See Section 3 in Boas) As suggested in Lecture 8 the formalism of eigenvalues/eigenvectors has many applications in physics, especially in
More informationUnforced Mechanical Vibrations
Unforced Mechanical Vibrations Today we begin to consider applications of second order ordinary differential equations. 1. Spring-Mass Systems 2. Unforced Systems: Damped Motion 1 Spring-Mass Systems We
More informationModal analysis of shear buildings
Modal analysis of shear buildings A comprehensive modal analysis of an arbitrary multistory shear building having rigid beams and lumped masses at floor levels is obtained. Angular frequencies (rad/sec),
More information11. Some applications of second order differential
October 3, 2011 11-1 11. Some applications of second order differential equations The first application we consider is the motion of a mass on a spring. Consider an object of mass m on a spring suspended
More informationALOHA FEATURE ARTICLES. One of the purposes of this newsletter is to present an interdisciplinary view of acoustics, shock, and vibration.
Acoustics Shock Vibration Signal Processing August 00 Newsletter ALOHA One of the purposes of this newsletter is to present an interdisciplinary view of acoustics, shock, and vibration. Potential topics
More informationChapter 5 Design. D. J. Inman 1/51 Mechanical Engineering at Virginia Tech
Chapter 5 Design Acceptable vibration levels (ISO) Vibration isolation Vibration absorbers Effects of damping in absorbers Optimization Viscoelastic damping treatments Critical Speeds Design for vibration
More informationAP PHYSICS 2012 SCORING GUIDELINES
AP PHYSICS 2012 SCORING GUIDELINES General Notes About 2012 AP Physics Scoring Guidelines 1. The solutions contain the most common method of solving the free-response questions and the allocation of points
More informationPhysical Acoustics. Hearing is the result of a complex interaction of physics, physiology, perception and cognition.
Physical Acoustics Hearing, auditory perception, or audition is the ability to perceive sound by detecting vibrations, changes in the pressure of the surrounding medium through time, through an organ such
More informationOscillations Simple Harmonic Motion
Oscillations Simple Harmonic Motion Lana Sheridan De Anza College Dec 1, 2017 Overview oscillations simple harmonic motion (SHM) spring systems energy in SHM pendula damped oscillations Oscillations and
More informationChapter 14 Oscillations. Copyright 2009 Pearson Education, Inc.
Chapter 14 Oscillations Oscillations of a Spring Simple Harmonic Motion Energy in the Simple Harmonic Oscillator Simple Harmonic Motion Related to Uniform Circular Motion The Simple Pendulum The Physical
More informationCHAPTER 12 TIME DOMAIN: MODAL STATE SPACE FORM
CHAPTER 1 TIME DOMAIN: MODAL STATE SPACE FORM 1.1 Introduction In Chapter 7 we derived the equations of motion in modal form for the system in Figure 1.1. In this chapter we will convert the modal form
More informationSection 3.7: Mechanical and Electrical Vibrations
Section 3.7: Mechanical and Electrical Vibrations Second order linear equations with constant coefficients serve as mathematical models for mechanical and electrical oscillations. For example, the motion
More informationChapter 14 Oscillations. Copyright 2009 Pearson Education, Inc.
Chapter 14 Oscillations 14-1 Oscillations of a Spring If an object vibrates or oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is called periodic. The
More informationDifferential Equations and Linear Algebra Exercises. Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS
Differential Equations and Linear Algebra Exercises Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS CHAPTER 1 Linear second order ODEs Exercises 1.1. (*) 1 The following differential
More informationChapter One Introduction to Oscillations
Chapter One Introduction to Oscillations This chapter discusses simple oscillations. This chapter also discusses simple functions to model oscillations like the sine and cosine functions. Part One Sine
More informationSession 1 : Fundamental concepts
BRUFACE Vibrations and Acoustics MA1 Academic year 17-18 Cédric Dumoulin (cedumoul@ulb.ac.be) Arnaud Deraemaeker (aderaema@ulb.ac.be) Exercise 1 Session 1 : Fundamental concepts Consider the following
More informationHarmonic Oscillator. Mass-Spring Oscillator Resonance The Pendulum. Physics 109 Experiment Number 12
Harmonic Oscillator Mass-Spring Oscillator Resonance The Pendulum Physics 109 Experiment Number 12 Outline Simple harmonic motion The vertical mass-spring system Driven oscillations and resonance The pendulum
More informationDynamics of Structures: Theory and Analysis
1. Free vibrations 2. Forced vibrations 3. Transient response 4. Damping mechanisms Dynamics of Structures: Theory and Analysis Steen Krenk Technical University of Denmark 5. Modal analysis I: Basic idea
More informationPhysics Homework 1
Physics 201 - Homewor 1 Ben Coy January 24, 2011 13.11 We are given the speed at the equilibrium position as 12ms 1. This is the maximum speed and is related to the amplitude by v max = Aω So we need to
More informationSimulating Two-Dimensional Stick-Slip Motion of a Rigid Body using a New Friction Model
Proceedings of the 2 nd World Congress on Mechanical, Chemical, and Material Engineering (MCM'16) Budapest, Hungary August 22 23, 2016 Paper No. ICMIE 116 DOI: 10.11159/icmie16.116 Simulating Two-Dimensional
More informationDesign Spectra. Reading Assignment Course Information Lecture Notes Pp Kramer Appendix B7 Kramer
Design Spectra Page 1 Design Spectra Reading Assignment Course Information Lecture Notes Pp. 73-75 Kramer Appendix B7 Kramer Other Materials Responsespectra.pdf (Chopra) ASCE 7-05.pdf Sakaria time history
More informationCRAIG-BAMPTON METHOD FOR A TWO COMPONENT SYSTEM Revision C
CRAIG-BAMPON MEHOD FOR A WO COMPONEN SYSEM Revision C By om Irvine Email: tom@vibrationdata.com May, 03 Introduction he Craig-Bampton method is method for reducing the size of a finite element model, particularly
More informationTranslational Mechanical Systems
Translational Mechanical Systems Basic (Idealized) Modeling Elements Interconnection Relationships -Physical Laws Derive Equation of Motion (EOM) - SDOF Energy Transfer Series and Parallel Connections
More informationChapter 14 Oscillations
Chapter 14 Oscillations If an object vibrates or oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is called periodic. The mass and spring system is a
More informationCE 6701 Structural Dynamics and Earthquake Engineering Dr. P. Venkateswara Rao
CE 6701 Structural Dynamics and Earthquake Engineering Dr. P. Venkateswara Rao Associate Professor Dept. of Civil Engineering SVCE, Sriperumbudur Difference between static loading and dynamic loading Degree
More informationMASS LOADING EFFECTS FOR HEAVY EQUIPMENT AND PAYLOADS Revision F
MASS LOADING EFFECTS FOR HEAVY EQUIPMENT AND PAYLOADS Revision F By Tom Irvine Email: tomirvine@aol.com May 19, 2011 Introduction Consider a launch vehicle with a payload. Intuitively, a realistic payload
More information1. Multiple Degree-of-Freedom (MDOF) Systems: Introduction
1. Multiple Degree-of-Freedom (MDOF) Systems: Introduction Lesson Objectives: 1) List examples of MDOF structural systems and state assumptions of the idealizations. 2) Formulate the equation of motion
More informationVibrationdata FEA Matlab GUI Package User Guide Revision A
Vibrationdata FEA Matlab GUI Package User Guide Revision A By Tom Irvine Email: tom@vibrationdata.com March 25, 2014 Introduction Matlab Script: vibrationdata_fea_preprocessor.zip vibrationdata_fea_preprocessor.m
More information