Content
CHAPTER 1 FUNDAMENTALS OF STRUCTURAL VIBRATIONS 1
1-1 Introduction 1
1-2 Definitions and Fundamental Aspects of Periodic Motion, 2
1-3 Differential Equations of Motion for Various Systems, 6
1-4 Lagrange's Equation, 11
1-5 Free Vibration of One-Degree Spring-Mass Systems, 16
1-6 Free Vibration with Viscous Damping, 19
1-7 Free Vibration with Coulomb Damping, 21
1-8 Free Vibration with Hysteresis Damping, 24
1-9 Free Vibration of Two-Degree Spring-Mass Systems, 25
1-10 Two-Degree Systems with Viscous Damping, 29
1-11 Free Vibration of Uniform Beams, 31
1-12 Orthogo_nality Properties of Normal Modes, 35
1-13 The Flexibility Matrix, 36
1-14 The Stiffness Matrix, 37
1-15 Computation of Stiffness Coefficients, 40
Problems, 44
CHAPTER 2 DYNAMIC RESPONSE OF SPRING-MASS SYSTEMS 49
2-1 Introduction, 49
2-2 Undamped Harmonic Excitations, 50
2-3 Damped Harmonic Excitations, 52
2-4 Impulse, 53
2-5 Dynamic Force of General Type, 54
2-6 Special Types of Forcing Function, 56
2-7 Numerical Analysis, 67
2-8 Elastoplastic Systems with One Degree of Freedom, 72
2-9 Systems with Two or More Degrees of Freedom, 80
2-10 Fourier Series, 84
Problems, 88
CHAPTER 3 IDEALIZED BEAMS, FRAMES, AND SIMPLE BUILDINGS 91
3-1 Introduction, 91
3-2 Idealized Beams, 92
3-3 Idealized One-Story Rigid Frames and Buildings, 94
3-4 Two-Story Rigid Frames and Buildings, 103
3-5 Multistory Rigid Frames and Buildings, 109
Problems, 115
CHAPTER 4 SYSTEMS WITH INFINITE DEGREES OF FREEDOM 121
4-1 Introduction, 121
4-2 Vibration of Single-Span Beams, 122
4-3 Initial Time Conditions for Beam Motions, 125
4-4 Vibration of Continuous Beams, 127
4-5 Dynamic Response of Beams, 135
4-6 Dynamic Response Due to Support. Motion, 141
4-7 Differential Equation of Motion for Thin Plates, 143
Problems, 146
CHAPTER 5 MODAL ANALYSIS 149
5-1 Introduction, 149
5-2 Modal Equations for Spring-Mass Systems, 150
5-3 Idealized Frames or Buildings, 154
5-4 Modal Equations for Infinite Degree of Freedom Systems, 159
5-5 Dynamic Response of Beams, 161
5-6 Moving Loads, 163
5-7 Modal Equation for Simply Supported Thin Plates, 165
5-8 Dynamic Response of Simply Supported Plates, 168
5-9 Dynamic Response of Lumped Parameter Systems, 171
5-10 Stodola's Method and Iteration Procedure, 173
5-11 Iteration Procedure Using Stiffness Coefficients, 180
5-12 Higher Frequencies of Vibration and Mode Shapes, 184
5-13 Vibration of Bridges, 188
5-14 Dynamic Response of Frames with Flexible Girders 193
Problems, 198
CHAPTER 6 METHODS OF VIBRATION 201
6-1 Introduction, 201
6-2 Rayleigh's Method, 202
6-3 Myklestad Method for Free Flexural Vibrations, 211
6-4 Transfer Matrices for Spring-Mass Systems, 216
6-5 Vibration of Spring-Mass Systems by Transfer Matrices, 221
6-6 Transfer Matrices for Flexural Systems, 225
6-7 Flexural Vibrations by Transfer Matrices, 230
6-8 Transfer Matrices for Continuous Beams, 234
6-9 The Dynamic Hinge Concept, 242
Problems, 247
CHAPTER 7 STRUCTURES WITH MEMBERS OF VARIABLE STIFFNESS 251
7-1 Introduction, 251
7-2 Dynamic Response of Beams, 253
7-3 Theory and Method of the Equivalent Systems, 253
7-4 Natural Frequencies and Mode Shapes for Beams, 266
7-5 Dynamic Response of Frames with Members of Variable Stiffness, 277
7-6 Beams on Elastic Supports, 283
Problems, 288
CHAPTER 8 FOURIER AND LAPLACE TRANSFORMS 295
8-1 Introduction, 295
8-2 Periodic Excitations and Discrete Spectra, 296
8-3 Nonperiodic Excitations, 299
8-4 Dynamic Response of Single-Degree Spring-Mass Systems, 303
8-5 Dynamic Response Due t9 a Unit Impulse, 308
8-6 Dynamic Response of Systems with Two or More Freedom, 310
8-7 Convolution, 313
Problems, 314
CHAPTER 9 VARIATIONAL APPROACH 317
9-1 Introduction, 317
9-2 Variational Properties, 318
9-3 Necessary Conditions for an Extremum, 320
9-4 Functionals with Movable Boundaries, 324
9-5 Vibration of Strings and Rods, 328
9-6 Free Transverse Vibration of Beams, 331
9-7 Longitudinal Vibrations of Uniform Elastic Beams, 334
9-8 Vibration of Plates, 337
Problems, 340
CHAPTER 10 APPROXIMATE METHODS FOR DYNAMIC RESPONSE 343
10-1 Introduction, 343
10-2 Fundamental Concepts, 344
10-3 Derivation of Transformation Factors, 346
10-4 Tabulation of Transformation Factors, 351
10-5 Charts for Elastoplastic Response, 361
10-6 Dynamic Response of Beams, 366
10-7 Dynamic Response of Concrete Slabs, 370
Problems, 376
CHAPTER 11 BLAST AND EARTHQUAKE 379
11-1 Introduction, 379
11-2 Dynamic Effects of Nuclear Explosions, 380
11-3 Dynamic Loading on Closed Rectangular Structures, 390
11-4 Computation of Dynamic Loading on Closed Structures, 394
11-5 Dynamic Loading on Rectangular Structures with Openings, 400
11 -6 Dynamic Loading on Open-Frame Structures, 403
11-7 Dynamic Loading on Structures with Cylindrical Surfaces, 405
11-8 Dynamic Analysis of Structures Subjected to Blast Loadings, 408
11-9 The Earthquake Problem, 411
11-10 Earthquake Intensity Scales, 414
11-11 Earthquake Response of Single-Story Structures, 416
11-12 Earthquake Response of Multistory Buildings , 419
11-13 Modal Analysis of Earthquake Response, 423
11-14 Inelastic Response of Multistory Structures, 429
11-15 Random Analysis for Earthquake Response, 431
11-16 Practical Considerations of Earthquake Design, 432 Problems, 433
CHAPTER 12 STOCHASTIC APPROACH TO STRUCTURAL 437
12-1 Introduction, 437
12-2 Probability, Random Variables, and Distribution Functions, 438
12-3 Expectations, 441
12-4 Correlation Functions, 442
12-5 Power Spectra Analysis, 443
12-6 Dynamic Response of Structural Systems Due to Random Excitations, 448
12-7 Probability as a Design Process, 456
Problems, 459
APPENDIX 461
REFERENCES AND BIBLIOGRAPHY 475
INDEX 481