| Preface | p. XV |
| List of Symbols | p. XIX |
| Introduction | p. 1 |
| Objectives of the study of structural dynamics | p. 1 |
| Importance of vibration analysis | p. 2 |
| Nature of exciting forces | p. 3 |
| Mathematical modeling of dynamic systems | p. 9 |
| Systems of units | p. 12 |
| Organization of the text | p. 13 |
| |
| Formulation of the Equations of Motion: Single-Degree-of-Freedom Systems | p. 21 |
| Introduction | p. 21 |
| Inertia forces | p. 21 |
| Resultants of inertia forces on a rigid body | p. 23 |
| Spring forces | p. 29 |
| Damping forces | p. 32 |
| Principle of virtual displacement | p. 33 |
| Formulation of the equations of motion | p. 38 |
| Modeling of multi-degree-of-freedom discrete parameter system | p. 54 |
| Effect of gravity load | p. 57 |
| Axial force effect | p. 60 |
| Effect of support motion | p. 65 |
| Formulation of the Equations of Motion: Multi-Degree-of-Freedom Systems | p. 73 |
| Introduction | p. 73 |
| Principal forces in multi-degree-of-freedom dynamic system | p. 75 |
| Formulation of the equations of motion | p. 84 |
| Transformation of coordinates | p. 107 |
| Finite element method | p. 111 |
| Finite element formulation of the flexural vibrations of a beam | p. 123 |
| Static condensation of stiffness matrix | p. 136 |
| Application of the Ritz method to discrete systems | p. 139 |
| Principles of Analytical Mechanics | p. 151 |
| Introduction | p. 151 |
| Generalized coordinates | p. 151 |
| Constraints | p. 156 |
| Virtual work | p. 159 |
| Generalized forces | p. 165 |
| Conservative forces and potential energy | p. 170 |
| Work function | p. 174 |
| Lagrangian multipliers | p. 178 |
| Virtual work equation for dynamical systems | p. 181 |
| Hamilton's equation | p. 186 |
| Lagrange's equation | p. 188 |
| Constraint conditions and lagrangian multipliers | p. 194 |
| Lagrange's equations for discrete multi-degree-of-freedom systems | p. 196 |
| Rayleigh's dissipation function | p. 198 |
| |
| Free Vibration Response: Single-Degree-of-Freedom System | p. 209 |
| Introduction | p. 209 |
| Undamped free vibration | p. 210 |
| Free vibrations with viscous damping | p. 220 |
| Damped free vibration with hysteretic damping | p. 231 |
| Damped free vibration with Coulomb damping | p. 233 |
| Forced Harmonic Vibrations: Single-Degree-of-Freedom System | p. 245 |
| Introduction | p. 245 |
| Procedures for the solution of the forced vibration equation | p. 246 |
| Undamped harmonic vibration | p. 248 |
| Resonant response of an undamped system | p. 253 |
| Damped harmonic vibration | p. 254 |
| Complex frequency response | p. 267 |
| Resonant response of a damped system | p. 272 |
| Rotating unbalanced force | p. 273 |
| Transmitted motion due to support movement | p. 279 |
| Transmissibility and vibration isolation | p. 284 |
| Vibration measuring instruments | p. 288 |
| Energy dissipated in viscous damping | p. 293 |
| Hysteretic damping | p. 297 |
| Complex stiffness | p. 301 |
| Coulomb damping | p. 301 |
| Measurement of damping | p. 304 |
| Response to General Dynamic Loading and Transient Response | p. 317 |
| Introduction | p. 317 |
| Response to an impulsive force | p. 317 |
| Response to general dynamic loading | p. 319 |
| REsponse to a step function load | p. 320 |
| Response to a ramp function load | p. 323 |
| Response to a step function load with rise time | p. 324 |
| Response to shock loading | p. 330 |
| Response to ground motion | p. 344 |
| Analysis of response by the phase plane diagram | p. 354 |
| Analysis of Single-Degree-of-Freedom Systems: Approximate and Numerical Methods | p. 361 |
| Introduction | p. 361 |
| Conservation of energy | p. 363 |
| Application of Rayleigh method to multi-degree-of-freedom systems | p. 368 |
| Improved Rayleigh method | p. 377 |
| Selection of an appropriate vibration shape | p. 383 |
| Systems with distributed mass and stiffness: Analysis of internal forces | p. 387 |
| Numerical evaluation of Duhamel's integral | p. 390 |
| Direct integration of the equations of motion | p. 399 |
| Integration based on piece-wise linear representation of the excitation | p. 399 |
| Derivation of general formulae | p. 404 |
| Constant-acceleration method | p. 405 |
| Newmark's [beta] method | p. 408 |
| Wilson-[theta] method | p. 416 |
| Methods based on difference expressions | p. 418 |
| Errors involved in numerical integration | p. 422 |
| Stability of the integration method | p. 423 |
| Selection of a numerical integration method | p. 431 |
| Selection of time step | p. 433 |
| Analysis of nonlinear response | p. 435 |
| Errors involved in numerical integration of nonlinear systems | p. 441 |
| Analysis of Response in the Frequency Domain | p. 453 |
| Transform methods of analysis | p. 453 |
| Fourier series representation of a periodic function | p. 454 |
| Response to a periodically applied load | p. 456 |
| Exponential form of fourier series | p. 460 |
| Complex frequency response function | p. 461 |
| Fourier integral representation of a nonperiodic load | p. 462 |
| Response to a nonperiodic load | p. 464 |
| Convolution integral and convolution theorem | p. 465 |
| Discrete Fourier transform | p. 468 |
| Discrete convolution and discrete convolution theorem | p. 471 |
| Comparison of continuous and discrete Fourier transforms | p. 473 |
| Application of discrete inverse transform | p. 481 |
| Comparison between continuous and discrete convolution | p. 487 |
| Discrete convolution of an infinite- and a finite-duration waveform | p. 492 |
| Corrective response superposition methods | p. 497 |
| Exponential window method | p. 515 |
| The fast Fourier transform | p. 520 |
| Theoretical background to fast Fourier transform | p. 521 |
| Computing speed of FFT convolution | p. 525 |
| |
| Free-Vibration Response: Multi-Degree-of-Freedom Systems | p. 533 |
| Introduction | p. 533 |
| Standard eigenvalue problem | p. 534 |
| Linearized eigenvalue problem and its properties | p. 535 |
| Expansion theorem | p. 540 |
| Rayleigh quotient | p. 541 |
| Solution of the undamped free-vibration problem | p. 545 |
| Mode superposition analysis of free-vibration response | p. 547 |
| Solution of the damped free-vibration problem | p. 553 |
| Additional orthogonality conditions | p. 564 |
| Damping orthogonality | p. 566 |
| Numerical Solution of the Eigenproblem | p. 581 |
| Introduction | p. 581 |
| Properties of standard eigenvalues and eigenvectors | p. 583 |
| Transformation of a linearized eigenvalue problem to the standard form | p. 584 |
| Transformation methods | p. 586 |
| Iteration methods | p. 602 |
| Determinant search method | p. 633 |
| Numerical solution of complex eigenvalue problem | p. 638 |
| Semi-definite or unrestrained systems | p. 648 |
| Selection of a method for the determination of eigenvalues | p. 658 |
| Forced Dynamic Response: Multi-Degree-of-Freedom Systems | p. 665 |
| Introduction | p. 665 |
| Normal coordinate transformation | p. 665 |
| Summary of mode superposition method | p. 668 |
| Complex frequency response | p. 673 |
| Vibration absorbers | p. 679 |
| Effect of support excitation | p. 681 |
| Forced vibration of unrestrained system | p. 691 |
| Analysis of Multi-Degree-of-Freedom Systems: Approximate and Numerical Methods | p. 701 |
| Introduction | p. 701 |
| Rayleigh-Ritz method | p. 702 |
| Application of Ritz method to forced vibration response | p. 720 |
| Direct integration of the equations of motion | p. 748 |
| Analysis in the frequency domain | p. 773 |
| Analysis of nonlinear response | p. 784 |
| |
| Formulation of the Equations of Motion: Continuous Systems | p. 795 |
| Introduction | p. 795 |
| Transverse vibrations of a beam | p. 796 |
| Transverse vibrations of a beam: variational formulation | p. 799 |
| Effect of damping resistance on transverse vibrations of a beam | p. 806 |
| Effect of shear deformation and rotatory inertia on the flexural vibrations of a beam | p. 807 |
| Axial vibrations of a bar | p. 810 |
| Torsional vibrations of a bar | p. 813 |
| Transverse vibrations of a string | p. 814 |
| Transverse vibrations of a shear beam | p. 815 |
| Transverse vibrations of a beam excited by support motion | p. 818 |
| Effect of axial force on transverse vibrations of a beam | p. 822 |
| Continuous Systems: Free Vibration Response | p. 829 |
| Introduction | p. 829 |
| Eigenvalue problem for the transverse vibrations of a beam | p. 830 |
| General eigenvalue problem for a continuous system | p. 834 |
| Expansion theorem | p. 838 |
| Frequencies and mode shapes for lateral vibrations of a beam | p. 839 |
| Effect of shear deformation and rotatory inertia on the frequencies of flexural vibrations | p. 848 |
| Frequencies and mode shapes for the axial vibrations of a bar | p. 852 |
| Frequencies and mode shapes for the transverse vibration of a string | p. 863 |
| Boundary conditions containing the eigenvalue | p. 865 |
| Free-vibration response of a continuous system | p. 871 |
| Undamped free transverse vibrations of a beam | p. 873 |
| Damped free transverse vibrations of a beam | p. 876 |
| Continuous Systems: Forced-Vibration Response | p. 879 |
| Introduction | p. 879 |
| Normal coordinate transformation: general case of an undamped system | p. 880 |
| Forced lateral vibration of a beam | p. 883 |
| Transverse vibrations of a beam under traveling load | p. 886 |
| Forced axial vibrations of a uniform bar | p. 889 |
| Normal coordinate transformation, damped case | p. 899 |
| Wave Propagation Analysis | p. 907 |
| Introduction | p. 907 |
| The phenomenon of wave propagation | p. 908 |
| Harmonic waves | p. 910 |
| One-dimensional wave equation and its solution | p. 914 |
| Propagation of waves in systems of finite extent | p. 919 |
| Reflection and refraction of waves at a discontinuity in the system properties | p. 928 |
| Characteristics of the wave equation | p. 933 |
| Wave dispersion | p. 935 |
| Answers to Selected Problems | p. 945 |
| Index | p. 959 |
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