Preface xi
About the Authors xiii
1 Introduction 1
1.1 Overview of Structural Dynamics 1
1.2 Dynamic Loads 2
1.2.1 Simple Harmonic Loads 2
1.2.2 Nonharmonic Periodic Loads 3
1.2.3 Impulsive Load 3
1.2.4 Irregular Dynamic Load 3
1.3 Characteristics of a Dynamic Problem 4
1.3.1 Methods of Discretization 6
1.3.2 Lumped Mass Procedure 6
1.3.3 Generalized Coordinate Procedure 7
1.3.4 Finite Element Method 9
1.4 Application of Structural Dynamics 10
1.4.1 Application of Structural Dynamics in Civil Engineering 10
1.4.2 Application of Structural Dynamics in Ocean Engineering 11
1.4.3 Application of Structural Dynamics in Aircraft Technology 14
Exercises 15
References 16
2 Establishment of the Structural Equation of Motion 17
2.1 General 17
2.1.1 Dynamic Freedom 17
2.1.2 Basics of Dynamic System 18
Inertia Force 18
Elastic Restoring Force 19
Damping Force 19
2.2 Formulation of the Equations of Motion 21
2.2.1 Direct Equilibration Using D’Alembert’s Principle 21
2.2.2 Principle of Virtual Displacements 23
2.2.3 Hamilton’s Principle 26
2.2.4 Lagrange’s Equations 30
2.3 Theory of Total Potential Energy Invariant Value of Elastic System Dynamics 32
2.3.1 The Main Idea of the Principle of Virtual Work 32
2.3.2 Derivation of the Principle of Total Potential Energy Invariant 34
2.4 Influence of Gravitational Forces 37
2.5 Influence of Support Excitation 38
Exercises 39
References 40
3 Single Degree of Freedom Systems 41
3.1 Response of Free Vibrations 41
3.1.1 Undamped Free Vibrations 43
3.1.2 Damped Free Vibrations 46
3.1.3 Damping and Its Measurement 52
3.2 Response to Harmonic Loading 57
3.2.1 Harmonic Vibration of an Undamped System 57
3.2.2 Harmonic Vibration of Damping System 62
3.2.3 Dynamic Amplification Coefficient 65
3.2.4 Resonance Reaction 68
3.2.5 Solution of Damping Ratio 70
3.3 Periodic Load Response 74
3.4 Impulsive Loading Response 80
3.4.1 Sine-Wave Impulse 80
3.4.2 Rectangular Impulse 82
3.4.3 Triangular Impulse 84
3.5 Response of Arbitrary Load 89
3.5.1 Duhamel Integral (Time-Domain Analysis) 89
3.5.2 Fourier Transform (Frequency-Domain Analysis) 95
3.6 Energy in Vibration 97
3.6.1 Energy in Free Vibration 97
3.6.2 Energy Dissipation of Viscous Damped System 99
3.6.3 Equivalent Viscous Damping 100
3.6.4 Complex Damping 103
3.6.5 Friction Damping 106
3.7 Structural Vibration Test 106
3.7.1 Introduction to Vibration Test 106
3.7.2 Exciting Equipment 107
3.7.3 Vibration Measuring Instrument 110
3.7.4 Data Acquisition and Analysis System 114
3.8 Vibration Isolation Principle 114
3.8.1 Active Vibration Isolation 114
3.8.2 Passive Vibration Isolation 116
3.9 Structural Vibration Induced Fatigue 121
3.9.1 Definition of Vibration Induced Fatigue 121
3.9.2 Characteristics of Vibration Induced Fatigue 122
Exercises 123
References 125
4 Multi-Degree of Freedom Systems 127
4.1 Two Degrees of Freedom System 128
4.1.1 Establishment of Motion Equation of Undamped Free Vibrations 128
4.1.2 Natural Frequency and Vibration Mode Shape 131
4.1.3 General Solutions of the Equations of Motion 134
4.2 Free Vibrations of Undamped System 135
4.2.1 Establishment of Motion Equation 135
4.2.2 Vibration Shape and Its Orthogonality 137
4.2.3 Generalized Mass and Generalized Stiffness 142
4.3 Practical Calculation Method of Dynamic Characteristics 146
4.3.1 Dunkerley Formula 147
4.3.2 Rayleigh Energy Method 150
4.3.3 Ritz Method 156
4.3.4 Matrix Iteration Method 160
4.3.5 Subspace Iteration Method 167
4.4 Mode Superposition Method for Damped System 172
4.4.1 Coordinate Coupling and Regular Coordinates 173
4.4.2 Damping Assumptions 174
4.4.3 Mode Superposition Method 179
4.5 Numerical Analysis of Damping System 185
4.5.1 Central Difference Method 186
4.5.2 Average Constant Acceleration Method 187
4.5.3 Linear Acceleration Method 191
4.5.4 Newmark-β Method 193
4.5.5 Wilson-θ Method 195
4.6 Stability and Accuracy Analysis of Stepwise Integration Method 199
4.6.1 Stability Analysis of Algorithm Solutions 202
4.6.2 Accuracy Analysis of Algorithm Solutions 202
Exercises 203
References 205
5 Distributed-Parameter System 207
5.1 Overview 207
5.2 Establish Differential Equations for Motion 208
5.2.1 Euler-Bernoulli Beam 208
5.2.2 Beam with Axial Pressures 210
5.2.3 Beam Flexure with Viscous Damping 211
5.2.4 Beam Axial Deformations without Damping 211
5.3 Free Vibration of a Beam 213
5.3.1 Decoupling the Boundary Conditions 214
5.3.2 Simply Supported Beam 215
5.3.3 Free-Free Beam 217
5.4 Orthogonality Relationships 221
5.5 Modal Decomposition 223
References 225
6 Stochastic Structural Vibrations 227
6.1 Overview 227
6.2 Stochastic Process 230
6.2.1 Concept of Stochastic Process 230
6.2.2 Probability Description of Stochastic Processes 232
6.2.3 The Numerical Characteristics of Stochastic Processes 234
6.2.4 Stationary Stochastic Process 248
6.2.5 Several Important Stochastic Processes 251
6.2.6 Stochastic Model of Seismic Ground Motion 253
6.3 Stochastic Response of Linear SDOF System 260
6.3.1 Time-Domain Analysis Method 260
6.3.2 Frequency-Domain Analysis Method 263
6.3.3 Cross-Correlation Function and Cross-Spectral Density of Excitation and Response 266
6.3.4 Fatigue Predictions for Narrowband Systems 270
6.4 Stochastic Response of Linear MDOF System 271
6.4.1 Direct Method 272
6.4.2 Vibration Mode Superposition Method 280
6.5 Nonlinear Structural Stochastic Response Analysis 291
6.5.1 Perturbation Method 292
6.5.2 Equivalent Linearization Method 294
6.6 State Space Method for Structural Stochastic Response Analysis 297
6.6.1 Basic Concept of State Space 298
6.6.2 SDOF System 299
6.6.3 MDOF System 302
Exercises 304
References 304
7 Research Topics of Structural Dynamics 305
7.1 Analysis of Structural Seismic Response 305
7.1.1 Brief Introduction to the Calculation Method 307
7.1.2 Horizontal Seismic Action of SDOF Elastic System 308
7.1.3 Seismic Response Spectrum 310
7.1.4 Vibration Mode Decomposition Method 314
7.1.5 Bottom Shearing Force Method 317
7.2 Structural Vibration Control 323
7.2.1 Concept and Classification 323
7.2.2 Vibration Reduction Technology of Viscoelastic Dampers 325
7.2.3 Rubber Base Isolation Technology 332
7.2.4 Vibration Reduction Technology of Magneto-Rheological Damper 337
7.3 Modal Analysis and Theory 341
7.3.1 Modal Parameters 342
7.3.2 Real Modal Analysis 344
7.3.3 Complex Modal Analysis 345
7.4 Structural Dynamic Damage Identification 350
7.4.1 Frequency Base Damage Identification Method 350
7.4.2 Modal Base Damage Identification Method 351
7.4.3 Damage Identification Method Based on Stiffness Variation 354
7.4.4 Damage Identification Method Based on Flexibility Change 355
7.4.5 Energy-Based Damage Identification Method 356
7.4.6 Prospects for Research on Dynamic Damage Identification 357
7.5 Nonlinear Problems of Dynamic Analysis 358
7.5.1 Physical Nonlinearity Problems in Dynamic Analysis 359
7.5.2 Geometric Nonlinearity Problems in Dynamic Analysis 362
7.6 Sub-Structure Method 365
7.6.1 Finite Element Analysis of Sub-Structure Method 365
7.6.2 Damage Identification by Sub-Structure Method 368
7.7 Dynamics of Offshore Structures 369
7.7.1 Descriptions of Offshore Waves 370
7.7.2 Introduction to Wave Spectra 370
7.7.3 Frequency Domain Analysis 371
Exercises 373
References 373
8 Structural Dynamics of Marine Pipeline and Riser 375
8.1 Overview 375
8.2 Environmental Conditions 376
8.2.1 General 376
8.2.2 Linear Wave Theory 377
8.2.3 Nonlinear Wave Theory 384
8.2.4 Current 384
8.3 Hydrodynamic Loads 386
8.3.1 Hydrodynamic Drag and Inertia Forces 386
8.3.2 Hydrodynamic Lift Forces 390
8.4 Structural Response Analysis 392
8.4.1 Global Deformation Due to Environmental Loads 392
8.4.2 Mass Matrices 394
8.4.3 Stiffness Matrices 397
8.4.4 Damping Matrices 399
8.4.5 Riser Deformation 400
8.5 Vortex Induced Vibrations 401
8.5.1 Introduction 401
8.5.2 Analysis of Vortex-Induced Vibration 404
8.5.3 Harmonic Model 406
8.5.4 Wake Oscillator Model 409
Exercises 415
References 415
Answers to Exercises 417
Index 443
