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CONTENTS
CHAPTER 1 SYSTEMS WITH ONE DEGREE OF FREEDOM = 1
 1.1 Free Harmonic Vibrations = 1
 1.2 Rotational Vibrations = 13
 1.3 Energy Method = 23
 1.4 Rayleigh Method = 31
 1.5 Beams and Shafts with Several Masses = 42
 1.6 Forced Vibrations : Steady State = 48
 1.7 Forced Vibrations : Transient State = 58
 1.8 Free Vibrations with Viscous Damping = 63
 1.9 Forced Vibrations with Viscous Damping = 72
 1.10 Equivalent Viscous Damping = 81
 1.11 General Periodic Disturbing Force = 89
 1.12 Arbitrary Disturbing Force = 97
 1.13 Arbitrary Support Motion = 110
 1.14 Response Spectra = 120
 1.15 Numerical Solutions for Response = 129
CHAPTER 2 SYSTEMS WITH NONLINEAR CHARACTERISTICS = 144
 2.1 Examples of Nonlinear Systems = 144
 2.2 Direct Integration for Velocity and Period = 159
 2.3 Approximate Methods for Free Vibrations = 168
 2.4 Forced Nonlinear Vibrations = 177
 2.5 Piecewise-Linear Systems = 186
 2.6 Numerical Solutions for Nonlinear Systems = 203
CHAPTER 3 SYSTEMS WITH TWO DEGREES OF FREEDOM = 219
 3.1 Examples of Two-Degree Systems = 219
 3.2 Action Equations : Stiffness Coefficients = 225
 3.3 Displacement Equations : Flexibility Coefficients = 231
 3.4 Inertial and Gravitational Coupling = 239
 3.5 Undamped Free Vibrations = 247
 3.6 Undamped Forced Vibrations = 259
 3.7 Free Vibrations with Viscous Damping = 267
 3.8 Forced Vibrations with Viscous Damping = 272
CHAPTER 4 SYSTEMS WITH MULTIPLE DEGREES OF FREEDOM = 279
 4.1 Introduction = 279
 4.2 Frequencies and Mode Shapes for Undamped Systems = 280
 4.3 Principal and Normal Coordinates = 296
 4.4 Normal-Mode Response to Initial Conditions = 303
 4.5 Normal-Mode Response to Applied Actions = 309
 4.6 Normal-Mode Response to Support Motions = 317
 4.7 Iteration Method for Frequencies and Mode Shapes = 327
 4.8 Damping in Multi-Degree Systems = 342
 4.9 Damped Response to Periodic Excitation = 346
 4.10 Transient Response of Damped Systems = 351
 4.11 Numerical Solutions for Transient Response = 355
CHAPTER 5 VIBRATIONS OF ELASTIC BODIES = 363
 5.1 Introduction = 363
 5.2 Free Longitudinal Vibrations of Prismatic Bars = 364
 5.3 Forced Longitudinal Response of Prismatic Bars = 373
 5.4 Normal-Mode Method for Prismatic Bars = 380
 5.5 Prismatic Bar with a Mass or Spring at the End = 387
 5.6 Bars Subjected to Longitudinal Support Motions = 395
 5.7 Torsional Vibrations of Circular Shafts = 401
 5.8 Transverse Vibrations of Stretched Wires = 408
 5.9 Transverse Vibrations of Prismatic Beams = 415
 5.10 Transverse Vibrations of a Simple Beam = 420
 5.11 Vibrations of Beams with Other End Conditions = 424
 5.12 Effects of Rotary Inertia and Shearing Deformations = 432
 5.13 Forced Response of a Simple Beam = 435
 5.14 Forced Response of Beams with Other End Conditions = 441
 5.15 Beams Subjected to Support Motions = 443
 5.16 Beams Traversed by Moving Loads = 448
 5.17 Effect of Axial Force on Vibrations of Beams = 453
 5.18 Beams on Elastic Supports or Elastic Foundations = 455
 5.19 Ritz Method for Calculating Frequencies = 459
 5.20 Vibrations of Nonprismatic Beams = 464
 5.21 Coupled Flexural and Torsional Vibrations of Beams = 471
 5.22 Vibrations of Circular Rings = 476
 5.23 Transverse Vibrations of Membranes = 481
 5.24 Transverse Vibrations of Plates = 492
APPENDIX : COMPUTER PROGRAMS = 503
 A.1 Introduction = 503
 A.2 Numerical Solutions for Linear Systems = 503
 A.3 Numerical Solutions for Nonlinear Systems = 504
 A.4 Iteration of Eigenvalues and Eigenvectors = 505
 A.5 Numerical Solutions for Multi-Degree Systems = 505
INDEX = 515