Dynamics of Structures

Dynamics of Structures This book covers structural dynamics from a theoretical and algorithmic approach. It covers systems with both single and multiple degrees-of-freedom. Numerous case studies are given to provide the reader with a deeper insight into the practicalities of the area, and the solutions to these case studies are given in terms of real-time and frequency in both geometric and modal spaces. Emphasis is also given to the subject of seismic loading. The text is based on many lectures on the subject of structural dynamics given at numerous institutions and thus will be an accessible and practical aid to students of the subject. Key features: Examines the effects of loads, impacts, and seismic forces on the materials used in the construction of buildings, bridges, tunnels, and more Structural dynamics is a critical aspect of the design of all engineered/designed structures and objects - allowing for accurate prediction of their ability to withstand service loading, and for knowledge of failure-causeing or critical loads

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