Dynamics of Structures

Preface vii

Chapter 1. Introduction 1

PART 1. SINGLE DEGREE OF FREEDOM SYSTEMS 25

Chapter 2. Equation of Motion 27

Chapter 3. Free Response 37

Chapter 4. Forced Response to Harmonic Loading 71

Chapter 5. Measurement of Damping 123

Chapter 6. Forced Response to Periodic Loading 141

Chapter 7. Response to Arbitrary Loading in the Time Domain 161

Chapter 8. Forced Response to Arbitrary Loading in Frequency Domain 195

Chapter 9. Direct Time Integration of Linear Systems 223

Chapter 10. Direct Time Integration of Nonlinear Systems 249

Chapter 11. Generalized Elementary Systems 271

Chapter 12. Response to Earthquake Excitation 307

PART 2. MULTI-DEGREES OF FREEDOM SYSTEMS 347

Chapter 13. Equations of Motion 349

Chapter 14. Finite Element Method 385

Chapter 15. Free Response of Conservative Systems 445

Chapter 16. Free Response of Non-conservative Systems 471

Chapter 17. Response to Arbitrary Loading by Modal Superposition 489

Chapter 18. Modal Superposition Response to Earthquake Excitation 511

Chapter 19. Properties of Eigenvalues and Eigenvectors 533

Chapter 20. Reduction of Coordinates 571

Chapter 21. Numerical Methods for Eigenproblems 607

Chapter 22. Direct Time Integration of Linear Systems 673

Chapter 23. Direct Time Integration of Nonlinear Systems 743

Appendix A: Complex Numbers 759

A.1. Algebric representation 759

A.2.Operations 760

A.3.Geometric representation 760

A.4. Trigonometric form 761

A.5.Roots 764

Bibliography 767

Index 775