Contents
Chapter 1 Overview of Structural Dynamics 1
1.1 Objective of structural dynamic analysis 1
1.2 Characteristics of structural dynamics 2
1.3 Classification of vibrations 3
1.4 Vibration problems in engineering 5
1.5 Procedures of dynamic response analysis of structures 6
Problems 9
References 9
Chapter 2 Formulation of Equations of Motion of Systems 10
2.1 System constraints 10
2.2 Representation of system configuration 13
2.3 Real displacements， possible displacements and virtual displacements 16
2.4 Generalized force 19
2.5 Conservative force and potential energy 23
2.6 Direct equilibrium method 25
2.7 Principle of virtual displacements 26
2.8 Lagranges equation 29
2.9 Hamiltons principle 33
2.10 Principle of total potential energy with a stationary value in elastic system dynamics
37
2.11 The ‘set-in-right-position’ rule for assembling system matrices and method of
computer implementation in Matlab 44
Problems 57
References 59
Chapter 3 Analysis of Dynamic Response of SDOF Systems 60
3.1 Analysis of free vibrations 60
3.2 Response of SDOF systems to harmonic loads 71
3.3 Vibration caused by base motion and vibration isolation81
3.4 Introduction to damping theory87
3.5 Evaluation of viscousdamping ratio 91
3.6 Response of SDOF systems to periodic loads 97
3.7 Response of SDOF systems to impulsive loads 99
3.8 Time domain analysis of dynamic response to arbitrary dynamic loads 111
3.9 Frequency domain analysis of dynamic response to arbitrary dynamic loads 113
Problems 118
References 120
Chapter 4 Analysis of Dynamic Response of MDOF Systems： Mode Superposition Method 121
4.1 Analysis of dynamic properties of MDOF systems 121
4.2 Coupling characteristics and uncoupling procedure of equations of MDOF systems
127
4.3 Analysis of free vibration response of undamped systems 132
4.4 Response of undamped systems to arbitrary dynamic loads 135
4.5 Response of damped systems to arbitrary dynamic loads 137
Problems 143
References 144
Chapter 5 Analysis of Dynamic Response of Continuous Systems： Straight beam 145
5.1 Differential equations of motion of undamped straight beam 146
5.2 Modal expansion of displacement and orthogonality of mode shapes of straight beam
147
5.3 Free vibration analysis of undamped straight beam 151
5.4 Forced vibration analysis of undamped straight beam 155
5.5 Forced vibration analysis of damped straight beam 158
Problems 161
References 162
Chapter 6 Approximate Evaluation of Natural Frequencies and Mode Shapes 163
6.1 Rayleigh energy method 163
6.2 Rayleigh-Ritz method 168
6.3 Matrix iteration method 172
6.4 Subspace iteration method 177
6.5 Reduction of degrees of freedom in dynamic analysis 183
Problems 187
References 188
Chapter 7 Step-by-step Integration Method 189
7.1 Basic idea of step-by-step integration method 189
7.2 Linear acceleration method191
7.3 Wilson-θ method 195
7.4 Newmark method 197
7.5 Stability and accuracy of stepbystep integration method 199
Problems 206
References 206
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