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Structural Dynamic Analysis with Generalized Damping Models: Analysis

Book Description

Since Lord Rayleigh introduced the idea of viscous damping in his classic work "The Theory of Sound" in 1877, it has become standard practice to use this approach in dynamics, covering a wide range of applications from aerospace to civil engineering. However, in the majority of practical cases this approach is adopted more for mathematical convenience than for modeling the physics of vibration damping.

Over the past decade, extensive research has been undertaken on more general "non-viscous" damping models and vibration of non-viscously damped systems. This book, along with a related book Structural Dynamic Analysis with Generalized Damping Models: Identification, is the first comprehensive study to cover vibration problems with general non-viscous damping. The author draws on his considerable research experience to produce a text covering: dynamics of viscously damped systems; non-viscously damped single- and multi-degree of freedom systems; linear systems with non-local and non-viscous damping; reduced computational methods for damped systems; and finally a method for dealing with general asymmetric systems. The book is written from a vibration theory standpoint, with numerous worked examples which are relevant across a wide range of mechanical, aerospace and structural engineering applications.

Contents

1. Introduction to Damping Models and Analysis Methods.

2. Dynamics of Undamped and Viscously Damped Systems.

3. Non-Viscously Damped Single-Degree-of-Freedom Systems.

4. Non-viscously Damped Multiple-Degree-of-Freedom Systems.

5. Linear Systems with General Non-Viscous Damping.

6. Reduced Computational Methods for Damped Systems

Table of Contents

  1. Cover
  2. Contents
  3. Dedication
  4. Title Page
  5. Copyright
  6. Preface
  7. Nomenclature
  8. Chapter 1: Introduction to Damping Models and Analysis Methods
    1. 1.1. Models of Damping
    2. 1.2. Modal Analysis of Viscously Damped Systems
    3. 1.3. Analysis of Non-Viscously Damped Systems
    4. 1.4. Identification of Viscous Damping
    5. 1.5. Identification of Non-Viscous Damping
    6. 1.6. Parametric Sensitivity of Eigenvalues and Eigenvectors
    7. 1.7. Motivation Behind this Book
    8. 1.8. Scope of The Book
  9. Chapter 2: Dynamics of Undamped and Viscously Damped Systems
    1. 2.1. Single-Degree-of-Freedom Undamped Systems
    2. 2.2. Single-Degree-of-Freedom Viscously Damped Systems
    3. 2.3. Multiple-Degree-of-Freedom Undamped Systems
    4. 2.4. Proportionally Damped Systems
    5. 2.5. Non-Proportionally Damped Systems
    6. 2.6. Rayleigh Quotient for Damped Systems
    7. 2.7. Summary
  10. Chapter 3: Non-Viscously Damped Single-Degree-of-Freedom Systems
    1. 3.1. The Equation of Motion
    2. 3.2. Conditions for Oscillatory Motion
    3. 3.3. Critical Damping Factors
    4. 3.4. Characteristics of the Eigenvalues
    5. 3.5. The Frequency Response Function
    6. 3.6. Characteristics of the Response Amplitude
    7. 3.7. Simplified Analysis of the Frequency Response Function
    8. 3.8. Summary
  11. Chapter 4: Non-viscously Damped Multiple-Degree-of-Freedom Systems
    1. 4.1. Choice of the Kernel Function
    2. 4.2. The Exponential Model for MDOF Non-Viscously Damped Systems
    3. 4.3. The State-Space Formulation
    4. 4.4. The Eigenvalue Problem
    5. 4.5. Forced Vibration Response
    6. 4.6. Numerical Examples
    7. 4.7. Direct Time-Domain Approach
    8. 4.8. Summary
  12. Chapter 5: Linear Systems with General Non-Viscous Damping
    1. 5.1. Existence of Classical Normal Modes
    2. 5.2. Eigenvalues and Eigenvectors
    3. 5.3. Transfer Function
    4. 5.4. Dynamic Response
    5. 5.5. Numerical Examples
    6. 5.6. Eigenrelations of Non-Viscously Damped Systems
    7. 5.7. Rayleigh Quotient for Non-Viscously Damped Systems
    8. 5.8. Summary
  13. Chapter 6: Reduced Computational Methods for Damped Systems
    1. 6.1. General Non-Proportionally Damped Systems with Viscous Damping
    2. 6.2. Single-Degree-of-Freedom Non-Viscously Damped Systems
    3. 6.3. Multiple-Degrees-of-Freedom Non-Viscously Damped Systems
    4. 6.4. Reduced Second-Order Approach for Non-Viscously Damped Systems
    5. 6.5. Summary
  14. Appendix
  15. Bibliography
  16. Author Index
  17. Index