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