Dynamics of Structures, Global Edition

Foreword xxi

Preface xxiii

Acknowledgments xxxi

 

PART I SINGLE-DEGREE-OF-FREEDOM SYSTEMS 1

 

1 Equations of Motion, Problem Statement, and Solution

Methods 3

1.1 Simple Structures 3

1.2 Single-Degree-of-Freedom System 7

1.3 Force—Displacement Relation 8

1.4 Damping Force 12

1.5 Equation of Motion: External Force 14

1.6 Mass—Spring—Damper System 19

1.7 Equation of Motion: Earthquake Excitation 23

1.8 Problem Statement and Element Forces 26

1.9 Combining Static and Dynamic Responses 28

1.10 Methods of Solution of the Differential Equation 28

1.11 Study of SDF Systems: Organization 33

Appendix 1: Stiffness Coefficients for a Flexural

Element 33

 

2 Free Vibration 39

2.1 Undamped Free Vibration 39

2.2 Viscously Damped Free Vibration 48

2.3 Energy in Free Vibration 56

2.4 Coulomb-Damped Free Vibration 57

 

3 Response to Harmonic and Periodic Excitations 65

Part A: Viscously Damped Systems: Basic Results 66

3.1 Harmonic Vibration of Undamped Systems 66

3.2 Harmonic Vibration with Viscous Damping 72

Part B: Viscously Damped Systems: Applications 85

3.3 Response to Vibration Generator 85

3.4 Natural Frequency and Damping from Harmonic

Tests 87

3.5 Force Transmission and Vibration Isolation 90

3.6 Response to Ground Motion and Vibration

Isolation 91

3.7 Vibration-Measuring Instruments 95

3.8 Energy Dissipated in Viscous Damping 99

3.9 Equivalent Viscous Damping 103

Part C: Systems with Nonviscous Damping 105

3.10 Harmonic Vibration with Rate-Independent

Damping 105

3.11 Harmonic Vibration with Coulomb Friction 109

Part D: Response to Periodic Excitation 113

3.12 Fourier Series Representation 114

3.13 Response to Periodic Force 114

Appendix 3: Four-Way Logarithmic Graph

Paper 118

 

4 Response to Arbitrary, Step, and Pulse Excitations 125

Part A: Response to Arbitrarily Time-Varying Forces 125

4.1 Response to Unit Impulse 126

4.2 Response to Arbitrary Force 127

Part B: Response to Step and Ramp Forces 129

4.3 Step Force 129

4.4 Ramp or Linearly Increasing Force 131

4.5 Step Force with Finite Rise Time 132

Part C: Response to Pulse Excitations 135

4.6 Solution Methods 135

4.7 Rectangular Pulse Force 137

4.8 Half-Cycle Sine Pulse Force 143

4.9 Symmetrical Triangular Pulse Force 148

4.10 Effects of Pulse Shape and Approximate Analysis for

Short Pulses 151

4.11 Effects of Viscous Damping 154

4.12 Response to Ground Motion 155

 

5 Numerical Evaluation of Dynamic Response 165

5.1 Time-Stepping Methods 165

5.2 Methods Based on Interpolation of Excitation 167

5.3 Central Difference Method 171

5.4 Newmark’s Method 174

5.5 Stability and Computational Error 180

5.6 Nonlinear Systems: Central Difference Method 183

5.7 Nonlinear Systems: Newmark’s Method 183

 

6 Earthquake Response of Linear Systems 197

6.1 Earthquake Excitation 197

6.2 Equation of Motion 203

6.3