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Tables of Contents for Structural Dynamics
Chapter/Section Title
Page #
Page Count
Preface
ix
Basic Concepts
1
12
Introduction to Structural Dynamics
1
1
Types of Dynamic Loads
2
1
Sources of Dynamic Loads
2
2
Distinguishing Features of a Dynamic Problem
4
1
Methodology for Dynamic Analysis
5
4
Types of Structural Vibration
9
1
Organization of the Text
10
2
Systems of Units
12
1
References
12
1
PART I Single-Degree-of-Freedom (SDOF) Systems
13
222
Equation of Motion and Natural Frequency
15
30
Fundamental Components of a Vibrating System
15
1
D'Alembert's Principle of Dynamic Equilibrium
16
5
The Energy Method
21
3
The Principle of Virtual Displacements
24
16
References
40
1
Notation
40
1
Problems
40
5
Undamped Free Vibration
45
33
Simple Harmonic Motion
45
5
Interpretation of the Solution
50
6
Equivalent Stiffness
56
10
Rayleigh Method
66
5
References
71
1
Notation
72
1
Problems
72
6
Damped Free Vibration
78
27
Free Vibration with Viscous Damping
78
8
Logarithmic Decrement
86
5
Hysteresis Damping
91
5
Coulomb Damping
96
4
References
100
1
Notation
100
1
Problems
101
4
Response to Harmonic Excitation
105
35
Forced Harmonic Response of Undamped Systems
105
5
Beating and Resonance
110
6
Forced Harmonic Vibrations with Viscous Damping
116
5
Effect of Damping Factor on Steady-State Response and Phase Angle
121
4
Harmonic Excitation Caused by Rotating Unbalance
125
3
Base Excitation
128
3
Vibration Isolation and Transmissibility
131
4
References
135
1
Notation
135
1
Problems
136
4
Response to Periodic and Arbitrary Dynamic Excitation
140
32
Response to Periodic Excitation
140
8
Response to Unit Impulse
148
2
Duhamel Integral
150
1
Response to Arbitrary Dynamic Excitation
151
11
Response Spectrum
162
4
References
166
1
Notation
167
1
Problems
167
5
Numerical Evaluation of Dynamic Response
172
35
Interpolation of the Excitation
172
5
Direct Integration of the Equation of Motion
177
1
Central Difference Method
177
6
Runge-Kutta Methods
183
6
Average Acceleration Method
189
5
Linear Acceleration Method
194
4
Response to Base Excitation
198
4
Response Spectra by Numerical Integration
202
2
References
204
1
Notaion
204
1
Problems
205
2
Frequency Domain Analysis
207
28
Alternative Forms of the Fourier Series
207
7
Discrete Fourier Transform
214
3
Fast Fourier Transform
217
6
Discrete Fourier Transform Implementation Considerations
223
6
Fourier Intergral
229
3
References
232
1
Notation
232
1
Problems
233
2
PART II Muti-Degree-of-Freedom (MDOF) Systems
235
200
General Property Matrices for Vibrating Systems
237
41
Flexibility Matrix
237
6
Stiffness Matrix
243
9
Inertia Properties: Mass Matrix
252
3
The Eigenproblem in Vibration Analysis
255
6
Static Condensation of the Stiffness Matrix
261
10
References
271
1
Notation
271
1
Problems
272
6
Equations of Motion and Undamped Free Vibration
278
49
Hamilton's Principle and the Lagrange Equations
279
9
Natural Vibration Frequencies
288
2
Natural Vibration Modes
290
6
Orthogonality of Natural Modes
296
1
Systems Admitting Rigid-Body Modes
297
7
Generalized Mass and Stiffness Matrics
304
4
Free Vibration Response to Initial Conditions
308
6
Approximate Methods for Estimating the Fundamental Frequency
314
7
References
321
1
Notation
321
1
Problems
322
5
Numerical Solution Methods for Natural Frequencies and Mode Shapes
327
30
General Solution Methods for Eigenproblems
327
2
Inverse Vector Iteration
329
10
Forward Vector Iteration
339
5
Generalized Jacobi Method
344
8
Solution Methods for Large Eigenproblems
352
1
References
353
1
Notation
353
1
Problems
354
3
Analysis of Dynamic Response by Mode Superposition
357
41
Mode Displacement Method for Undamped Systems
357
9
Modal Participation Factor
366
3
Mode Superposition Solution for Solution for Systems with Classical Damping
369
4
Numerical Evaluation of Modal Response
373
5
Normal Mode Response to Support Motions
378
6
Response Spectrum Analysis
384
2
Mode Acceleration Method
386
5
References
391
1
Notation
392
1
Problems
393
5
Analysis of Dynamic Response by Direct Integration
398
37
Basic Concepts of Direct Integration Methods
398
1
The Central Difference Method
399
8
The Wilson-θ Method
407
10
The Newmark Method
417
3
Practical Considerations for Damping
420
7
Stability and Accuracy of Direct Integration Methods
427
1
Direct Integration Versus Mode Superposition
428
1
Referenreces
429
1
Notation
430
1
Problems
431
4
PART III Continuous Systems
435
60
Vibrations of Continuous Systems
437
58
Longitudinal Vibration of a Uniforms Rod
438
5
Transverse Vibration of a Pretensioned Cable
443
2
Free Transverse Vibration of Uniform Beams
445
13
Orthogonality of Normal Modes
458
2
Undamped Forced Vibration of Beams by Mode Superposition
460
7
Approximate Methods
467
21
References
488
1
Notation
488
1
Problems
489
6
PART IV Nonlinear Dynamic Response
495
54
Analysis of Nonlinear Response
497
52
Classification of Nonlinear Analyses
498
5
Systems With Nonlinear Characteristics
503
3
Formulation of Incremental Equations of Equilibrium
506
2
Numerical Solution of Nonlinear Equilibrium Equations
508
9
Response of Elastoplastic SDOF Systems
517
15
Repsonse of Elastoplastic MDOF Systems
532
12
References
544
1
Notation
544
2
Problems
546
3
PART V Practical Applications
549
248
Elastic Wave Propagation in Solids
551
33
Stress and Strain at a Point
552
3
Constitutive Relations
555
8
Equations of Motion
563
1
Stress Wave Propagation
563
8
Applications
571
11
References
582
1
Problems
583
1
Earthquakes and Earthquake Ground Motion
584
17
Causes of Earthquakes
584
2
Faults
586
1
Seismic Waves
587
2
Earthquake Intensity
589
3
Earthquake Magnitude
592
2
Seismicity
594
2
Earthquake Ground Motion
596
3
Earthquake Damage Mechanisms
599
1
References
599
1
Notation
600
1
Earthquake Response of Structures
601
81
Time-History Analysis: Basic Concepts
602
8
Earthquake Response Spectra
610
6
Earthquake Design Spectra
616
16
Response of MDOF Systems
632
16
Generalized SDOF Systems
648
12
In-Building Response Spectrum
660
5
Inelastic Response
665
8
Seismic Design Codes
673
2
References
675
1
Notation
676
2
Problems
678
4
Blast Loads on Structures
682
28
Sources of Blast Loads
682
1
Shock Waves
683
6
Determination of Blast Loads
689
6
Strain-Rate Effects
695
6
Approximate Solution Technique for SDOF Systems
701
5
Refereces
706
1
Problems
707
1
Notations
708
2
Basic Concepts of Wind Waves
710
42
Linear Wave Theory
710
9
Nonlinear Waves
719
3
Wave Transformations
722
8
Wave Statistics
730
11
Wave Information Damping
741
7
References
748
1
Notation
749
1
Problems
750
2
Response of Structures to Waves
752
45
Morison Equation
753
7
Force Coefficients
760
8
Linearized Morison Equation
768
4
Inclined Cylinders
772
4
Transverse Lift Forces
776
2
Froude-Krylov Theory
778
1
Diffraction Theory: The Scattering Problem
779
9
Diffraction Theory: The Radiation Problem
788
6
References
794
1
Notation
794
1
Problems
795
2
Appendix A
797
2
Appendix B
799
2
Index
801