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Prentice Hall Professional Technical Reference
Dynamics of Structures

Dynamics of Structures

by J. L. Humar


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Product Details

ISBN-13: 9780132220682
Publisher: Prentice Hall Professional Technical Reference
Publication date: 09/01/1989
Series: Prentice Hall International Series in Civil Engineering and Engineering Mechanics
Pages: 672
Product dimensions: 6.50(w) x 1.50(h) x 9.50(d)

Table of Contents

List of SymbolsXIX
1.1Objectives of the study of structural dynamics1
1.2Importance of vibration analysis2
1.3Nature of exciting forces3
1.4Mathematical modeling of dynamic systems9
1.5Systems of units12
1.6Organization of the text13
Part 1
2Formulation of the Equations of Motion: Single-Degree-of-Freedom Systems21
2.2Inertia forces21
2.3Resultants of inertia forces on a rigid body23
2.4Spring forces29
2.5Damping forces32
2.6Principle of virtual displacement33
2.7Formulation of the equations of motion38
2.8Modeling of multi-degree-of-freedom discrete parameter system54
2.9Effect of gravity load57
2.10Axial force effect60
2.11Effect of support motion65
3Formulation of the Equations of Motion: Multi-Degree-of-Freedom Systems73
3.2Principal forces in multi-degree-of-freedom dynamic system75
3.3Formulation of the equations of motion84
3.4Transformation of coordinates107
3.5Finite element method111
3.6Finite element formulation of the flexural vibrations of a beam123
3.7Static condensation of stiffness matrix136
3.8Application of the Ritz method to discrete systems139
4Principles of Analytical Mechanics151
4.2Generalized coordinates151
4.4Virtual work159
4.5Generalized forces165
4.6Conservative forces and potential energy170
4.7Work function174
4.8Lagrangian multipliers178
4.9Virtual work equation for dynamical systems181
4.10Hamilton's equation186
4.11Lagrange's equation188
4.12Constraint conditions and lagrangian multipliers194
4.13Lagrange's equations for discrete multi-degree-of-freedom systems196
4.14Rayleigh's dissipation function198
Part 2
5Free Vibration Response: Single-Degree-of-Freedom System209
5.2Undamped free vibration210
5.3Free vibrations with viscous damping220
5.4Damped free vibration with hysteretic damping231
5.5Damped free vibration with Coulomb damping233
6Forced Harmonic Vibrations: Single-Degree-of-Freedom System245
6.2Procedures for the solution of the forced vibration equation246
6.3Undamped harmonic vibration248
6.4Resonant response of an undamped system253
6.5Damped harmonic vibration254
6.6Complex frequency response267
6.7Resonant response of a damped system272
6.8Rotating unbalanced force273
6.9Transmitted motion due to support movement279
6.10Transmissibility and vibration isolation284
6.11Vibration measuring instruments288
6.12Energy dissipated in viscous damping293
6.13Hysteretic damping297
6.14Complex stiffness301
6.15Coulomb damping301
6.16Measurement of damping304
7Response to General Dynamic Loading and Transient Response317
7.2Response to an impulsive force317
7.3Response to general dynamic loading319
7.4REsponse to a step function load320
7.5Response to a ramp function load323
7.6Response to a step function load with rise time324
7.7Response to shock loading330
7.8Response to ground motion344
7.9Analysis of response by the phase plane diagram354
8Analysis of Single-Degree-of-Freedom Systems: Approximate and Numerical Methods361
8.2Conservation of energy363
8.3Application of Rayleigh method to multi-degree-of-freedom systems368
8.4Improved Rayleigh method377
8.5Selection of an appropriate vibration shape383
8.6Systems with distributed mass and stiffness: Analysis of internal forces387
8.7Numerical evaluation of Duhamel's integral390
8.8Direct integration of the equations of motion399
8.9Integration based on piece-wise linear representation of the excitation399
8.10Derivation of general formulae404
8.11Constant-acceleration method405
8.12Newmark's [beta] method408
8.13Wilson-[theta] method416
8.14Methods based on difference expressions418
8.15Errors involved in numerical integration422
8.16Stability of the integration method423
8.17Selection of a numerical integration method431
8.18Selection of time step433
8.19Analysis of nonlinear response435
8.20Errors involved in numerical integration of nonlinear systems441
9Analysis of Response in the Frequency Domain453
9.1Transform methods of analysis453
9.2Fourier series representation of a periodic function454
9.3Response to a periodically applied load456
9.4Exponential form of fourier series460
9.5Complex frequency response function461
9.6Fourier integral representation of a nonperiodic load462
9.7Response to a nonperiodic load464
9.8Convolution integral and convolution theorem465
9.9Discrete Fourier transform468
9.10Discrete convolution and discrete convolution theorem471
9.11Comparison of continuous and discrete Fourier transforms473
9.12Application of discrete inverse transform481
9.13Comparison between continuous and discrete convolution487
9.14Discrete convolution of an infinite- and a finite-duration waveform492
9.15Corrective response superposition methods497
9.16Exponential window method515
9.17The fast Fourier transform520
9.18Theoretical background to fast Fourier transform521
9.19Computing speed of FFT convolution525
Part 3
10Free-Vibration Response: Multi-Degree-of-Freedom Systems533
10.2Standard eigenvalue problem534
10.3Linearized eigenvalue problem and its properties535
10.4Expansion theorem540
10.5Rayleigh quotient541
10.6Solution of the undamped free-vibration problem545
10.7Mode superposition analysis of free-vibration response547
10.8Solution of the damped free-vibration problem553
10.9Additional orthogonality conditions564
10.10Damping orthogonality566
11Numerical Solution of the Eigenproblem581
11.2Properties of standard eigenvalues and eigenvectors583
11.3Transformation of a linearized eigenvalue problem to the standard form584
11.4Transformation methods586
11.5Iteration methods602
11.6Determinant search method633
11.7Numerical solution of complex eigenvalue problem638
11.8Semi-definite or unrestrained systems648
11.9Selection of a method for the determination of eigenvalues658
12Forced Dynamic Response: Multi-Degree-of-Freedom Systems665
12.2Normal coordinate transformation665
12.3Summary of mode superposition method668
12.4Complex frequency response673
12.5Vibration absorbers679
12.6Effect of support excitation681
12.7Forced vibration of unrestrained system691
13Analysis of Multi-Degree-of-Freedom Systems: Approximate and Numerical Methods701
13.2Rayleigh-Ritz method702
13.3Application of Ritz method to forced vibration response720
13.4Direct integration of the equations of motion748
13.5Analysis in the frequency domain773
13.6Analysis of nonlinear response784
Part 4
14Formulation of the Equations of Motion: Continuous Systems795
14.2Transverse vibrations of a beam796
14.3Transverse vibrations of a beam: variational formulation799
14.4Effect of damping resistance on transverse vibrations of a beam806
14.5Effect of shear deformation and rotatory inertia on the flexural vibrations of a beam807
14.6Axial vibrations of a bar810
14.7Torsional vibrations of a bar813
14.8Transverse vibrations of a string814
14.9Transverse vibrations of a shear beam815
14.10Transverse vibrations of a beam excited by support motion818
14.11Effect of axial force on transverse vibrations of a beam822
15Continuous Systems: Free Vibration Response829
15.2Eigenvalue problem for the transverse vibrations of a beam830
15.3General eigenvalue problem for a continuous system834
15.4Expansion theorem838
15.5Frequencies and mode shapes for lateral vibrations of a beam839
15.6Effect of shear deformation and rotatory inertia on the frequencies of flexural vibrations848
15.7Frequencies and mode shapes for the axial vibrations of a bar852
15.8Frequencies and mode shapes for the transverse vibration of a string863
15.9Boundary conditions containing the eigenvalue865
15.10Free-vibration response of a continuous system871
15.11Undamped free transverse vibrations of a beam873
15.12Damped free transverse vibrations of a beam876
16Continuous Systems: Forced-Vibration Response879
16.2Normal coordinate transformation: general case of an undamped system880
16.3Forced lateral vibration of a beam883
16.4Transverse vibrations of a beam under traveling load886
16.5Forced axial vibrations of a uniform bar889
16.6Normal coordinate transformation, damped case899
17Wave Propagation Analysis907
17.2The phenomenon of wave propagation908
17.3Harmonic waves910
17.4One-dimensional wave equation and its solution914
17.5Propagation of waves in systems of finite extent919
17.6Reflection and refraction of waves at a discontinuity in the system properties928
17.7Characteristics of the wave equation933
17.8Wave dispersion935
Answers to Selected Problems945

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