Cover	1
	Title Page	5
	Copyright	6
	Contents	7
	Series Preface	11
	Preface	13
	Chapter 1 A Crash Course on Lagrangian Dynamics	17
	1.1 Objectives	17
	1.2 Concept of "Equation of Motion"	17
	1.3 Generalized Coordinates	21
	1.4 Admissible Variations	29
	1.5 Degrees of Freedom	32
	1.6 Virtual Work and Generalized Forces	33
	1.7 Lagrangian	40
	1.8 Lagrange's Equation	40
	1.9 Procedure for Deriving Equation(s) of Motion	40
	1.10 Worked Examples	41
	1.10.1 Systems Containing Only Particles	41
	1.10.2 Systems Containing Rigid Bodies	54
	1.11 Linearization of Equations of Motion	73
	1.11.1 Equilibrium Position(s)	74
	1.11.2 Linearization	75
	1.11.3 Observations and Further Discussions	78
	1.12 Chapter Summary	79
	Chapter 2 Vibrations of Single-DOF Systems	97
	2.1 Objectives	97
	2.2 Types of Vibration Analyses	97
	2.3 Free Vibrations of Undamped System	99
	2.3.1 General Solution for Homogeneous Differential Equation	99
	2.3.2 Basic Vibration Terminologies	101
	2.3.3 Determining Constants via Initial Conditions	103
	2.4 Free Vibrations of Damped Systems	109
	2.5 Using Normalized Equation of Motion	110
	2.5.1 Normalization of Equation of Motion	110
	2.5.2 Classification of Vibration Systems	111
	2.5.3 Free Vibration of Underdamped Systems	112
	2.5.4 Free Vibration of Critically Damped System	116
	2.5.5 Free Vibration of Overdamped System	118
	2.6 Forced Vibrations I: Steady-State Responses	124
	2.6.1 Harmonic Loading	124
	2.6.2 Mechanical Significance of Steady-State Solution	126
	2.6.3 Other Examples of Harmonic Loading	131
	2.6.4 General Periodic Loading	140
	2.7 Forced Vibrations II: Transient Responses	149
	2.7.1 Transient Response to Periodic Loading	150
	2.7.2 General Loading: Direct Analytical Method	155
	2.7.3 Laplace Transform Method	162
	2.7.4 Decomposition Method	166
	2.7.5 Convolution Integral Method	175
	2.8 Chapter Summary	188
	2.8.1 Free Vibrations of Single-DOF Systems	188
	2.8.2 Steady-State Responses of Single-DOF Systems	189
	2.8.3 Transient Responses of Single-DOF Systems	190
	Chapter 3 Lumped-Parameter Modeling	202
	3.1 Objectives	202
	3.2 Modeling	202
	3.3 Idealized Elements	203
	3.3.1 Mass Elements	203
	3.3.2 Spring Elements	204
	3.3.3 Damping Elements	205
	3.4 Lumped-Parameter Modeling of Simple Components and Structures	206
	3.4.1 Equivalent Spring Constants	207
	3.4.2 Equivalent Masses	220
	3.4.3 Damping Models	228
	3.5 Alternative Methods	234
	3.5.1 Castigliano Method for Equivalent Spring Constants	234
	3.5.2 Rayleigh-Ritz Method for Equivalent Masses	239
	3.5.3 Rayleigh-Ritz Method for Equivalent Spring Constants	243
	3.5.4 Rayleigh-Ritz Method for Natural Frequencies	246
	3.5.5 Determining Lumped Parameters Through Experimental Measurements	247
	3.6 Examples with Lumped-Parameter Models	249
	3.7 Chapter Summary	268
	Chapter 4 Vibrations of Multi-DOF Systems	285
	4.1 Objectives	285
	4.2 Matrix Equation of Motion	285
	4.3 Modal Analysis: Natural Frequencies and Mode Shapes	289
	4.4 Free Vibrations	300
	4.4.1 Free Vibrations of Undamped Systems	300
	4.4.2 Free Vibrations of Undamped Unconstrained Systems	309
	4.4.3 Free Vibrations of Systems of Many DOFs	312
	4.5 Eigenvalues and Eigenvectors	321
	4.5.1 Standard Eigenvalue Problem	321
	4.5.2 Generalized Eigenvalue Problem	322
	4.6 Coupling, Decoupling, and Principal Coordinates	323
	4.6.1 Types of Coupling	323
	4.6.2 Principal Coordinates	323
	4.6.3 Decoupling Method for Free-Vibration Analysis	326
	4.7 Forced Vibrations I: Steady-State Responses	335
	4.8 Forced Vibrations II: Transient Responses	344
	4.8.1 Direct Analytical Method	344
	4.8.2 Decoupling Method	347
	4.8.3 Laplace Transform Method	363
	4.8.4 Convolution Integral Method	365
	4.9 Chapter Summary	373
	4.9.1 Modal Analyses	373
	4.9.2 Free Vibrations of Multi-DOF Systems	373
	4.9.3 Steady-State Responses of Multi-DOF Systems	375
	4.9.4 Transient Responses of Multi-DOF Systems	375
	References	385
	Chapter 5 Vibration Analyses Using Finite Element Method	386
	5.1 Objectives	386
	5.2 Introduction to Finite Element Method	386
	5.2.1 Lagrangian Dynamics Formulation of FEM Model	387
	5.2.2 Matrix Formulation	390
	5.3 Finite Element Analyses of Beams	394
	5.3.1 Formulation of Beam Element	395
	5.3.2 Implementation Using MatLab	399
	5.3.3 Generalization: Large-Scale Finite Element Simulations	408
	5.3.4 Damping Models in Finite Element Modeling	410
	5.4 Vibration Analyses Using SolidWorks	411
	5.4.1 Introduction to SolidWorks Simulation	412
	5.4.2 Static Analysis	414
	5.4.3 Modal Analysis	431
	5.4.4 Harmonic Vibration Analysis	435
	5.4.5 Transient Vibration Analysis	441
	5.5 Chapter Summary	444
	5.5.1 Finite Element Formulation	444
	5.5.2 Using Commercial Finite Element Analysis Software	445
	Appendix A Review of Newtonian Dynamics	449
	A.1 Kinematics	449
	A.1.1 Kinematics of a Point or a Particle	449
	A.1.2 Relative Motions	451
	A.1.3 Kinematics of a Rigid Body	452
	A.2 Kinetics	453
	A.2.1 Newton-Euler Equations	453
	A.2.2 Energy Principles	454
	A.2.3 Momentum Principles	455
	Appendix B A Primer on MatLab	456
	B.1 Matrix Computations	456
	B.1.1 Commands and Statements	456
	B.1.2 Matrix Generation	457
	B.1.3 Accessing Matrix Elements and Submatrices	458
	B.1.4 Operators and Elementary Functions	460
	B.1.5 Flow Controls	462
	B.1.6 M-Files, Scripts, and Functions	465
	B.1.7 Linear Algebra	468
	B.2 Plotting	470
	B.2.1 Two-Dimensional Curve Plots	470
	B.2.2 Three-Dimensional Curve Plots	472
	B.2.3 Three-Dimensional Surface Plots	473
	Appendix C Tables of Laplace Transform	475
	C.1 Properties of Laplace Transform	475
	C.2 Function Transformations	475
	Index	477
	EULA	483