Mechanical Vibrations: A State-Space Perspective

Amir Danesh, Yi Wu

This book tackled the topics discussed in a typical vibrations (undergraduate or graduate) course through the state-space approach, which until now had been used more extensively in the field of controls. A consistent framework has been developed based on this approach to study various vibration problems regardless of the degree of freedoms, free or forced vibration, or types of excitations. The textbook also includes animations visualizing virtually every vibration scenario discussed and numerous interactive questions (multiple-choice , matching, sorting, short answer, etc) interspersed within the text to aid in the student’s understanding of the presented material.

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Table of Contents for Mechanical Vibrations: A State-Space Perspective

Chapter 1: Introduction to Vibration
Chapter 2: Equations of Motion and Model Representation
Chapter 3: Free Vibration of Single-Degree-of-Freedom-Systems
Chapter 4: Forced Vibration of Single-Degree-of-Freedom Systems
Chapter 5: Vibration of Multi-Degree-of-Freedom Systems
Chapter 6: Passive Vibration Control
Chapter 7: Distributed-Parameter (Continuous) Systems
Chapter 8: Finite Element Method
Appendix A: Problem-Solving Approach
Appendix B: Review of Matrices
Appendix C: Solving Ordinary Differential Equations in MATLAB
Appendix D: Derivation of the Total Response of an SDOF system using the State-Space Representation
Appendix E: Derivation of MDOF System Parameters from the State-Space Representation
Appendix F: State-Space Representation of MDOF Systems with a Non-Invertible Mass Matrix