Structural dynamic analysis with generalized damping models analysis
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 c...
| Autor principal: | |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
London, England ; Hoboken, New Jersey :
ISTE Ltd
2014.
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| Edición: | 1st edition |
| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009628104606719 |
Tabla de Contenidos:
- Cover
- Title page
- Table of Contents
- Preface
- Nomenclature
- Chapter 1. Introduction to Damping Models and Analysis Methods
- 1.1. Models of damping
- 1.1.1. Single-degree-of-freedom systems
- 1.1.2. Continuous systems
- 1.1.3. Multiple-degrees-of-freedom systems
- 1.1.4. Other studies
- 1.2. Modal analysis of viscously damped systems
- 1.2.1. The state-space method
- 1.2.2. Methods in the configuration space
- 1.3. Analysis of non-viscously damped systems
- 1.3.1. State-space-based methods
- 1.3.2. Time-domain-based methods
- 1.3.3. Approximate methods in the configuration space
- 1.4. Identification of viscous damping
- 1.4.1. Single-degree-of-freedom systems
- 1.4.2. Multiple-degrees-of-freedom systems
- 1.5. Identification of non-viscous damping
- 1.6. Parametric sensitivity of eigenvalues and eigenvectors
- 1.6.1. Undamped systems
- 1.6.2. Damped systems
- 1.7. Motivation behind this book
- 1.8. Scope of the book
- Chapter 2. Dynamics of Undamped and Viscously Damped Systems
- 2.1. Single-degree-of-freedom undamped systems
- 2.1.1. Natural frequency
- 2.1.2. Dynamic response
- 2.2. Single-degree-of-freedom viscously damped systems
- 2.2.1. Natural frequency
- 2.2.2. Dynamic response
- 2.3. Multiple-degree-of-freedom undamped systems
- 2.3.1. Modal analysis
- 2.3.2. Dynamic response
- 2.4. Proportionally damped systems
- 2.4.1. Condition for proportional damping
- 2.4.2. Generalized proportional damping
- 2.4.3. Dynamic response
- 2.5. Non-proportionally damped systems
- 2.5.1. Free vibration and complex modes
- 2.5.2. Dynamic response
- 2.6. Rayleigh quotient for damped systems
- 2.6.1. Rayleigh quotients for discrete systems
- 2.6.2. Proportional damping
- 2.6.3. Non-proportional damping
- 2.6.4. Application of Rayleigh quotients
- 2.6.5. Synopses
- 2.7. Summary.
- Chapter 3. Non-Viscously Damped Single-Degree-of-Freedom Systems
- 3.1. The equation of motion
- 3.2. Conditions for oscillatory motion
- 3.3. Critical damping factors
- 3.4. Characteristics of the eigenvalues
- 3.4.1. Characteristics of the natural frequency
- 3.4.2. Characteristics of the decay rate corresponding to the oscillating mode
- 3.4.3. Characteristics of the decay rate corresponding to the non-oscillating mode
- 3.5. The frequency response function
- 3.6. Characteristics of the response amplitude
- 3.6.1. The frequency for the maximum response amplitude
- 3.6.2. The amplitude of the maximum dynamic response
- 3.7. Simplified analysis of the frequency response function
- 3.8. Summary
- Chapter 4. Non-viscously Damped Multiple-Degree-of-Freedom Systems
- 4.1. Choice of the kernel function
- 4.2. The exponential model for MDOF non-viscously damped systems
- 4.3. The state-space formulation
- 4.3.1. Case A: all coefficient matrices are of full rank
- 4.3.2. Case B: coefficient matrices are rank deficient
- 4.4. The eigenvalue problem
- 4.4.1. Case A: all coefficient matrices are of full rank
- 4.4.2. Case B: coefficient matrices are rank deficient
- 4.5. Forced vibration response
- 4.5.1. Frequency domain analysis
- 4.5.2. Time-domain analysis
- 4.6. Numerical examples
- 4.6.1. Example 1: SDOF system with non-viscous damping
- 4.6.2. Example 2: a rank-deficient system
- 4.7. Direct time-domain approach
- 4.7.1. Integration in the time domain
- 4.7.2. Numerical realization
- 4.7.3. Summary of the method
- 4.7.4. Numerical examples
- 4.8. Summary
- Chapter 5. Linear Systems with General Non-Viscous Damping
- 5.1. Existence of classical normal modes
- 5.1.1. Generalization of proportional damping
- 5.2. Eigenvalues and eigenvectors
- 5.2.1. Elastic modes
- 5.2.2. Non-viscous modes.
- 5.2.3. Approximations for lightly damped systems
- 5.3. Transfer function
- 5.3.1. Eigenvectors of the dynamic stiffness matrix
- 5.3.2. Calculation of the residues
- 5.3.3. Special cases
- 5.4. Dynamic response
- 5.4.1. Summary of the method
- 5.5. Numerical examples
- 5.5.1. The system
- 5.5.2. Example 1: exponential damping
- 5.5.3. Example 2: GHM damping
- 5.6. Eigenrelations of non-viscously damped systems
- 5.6.1. Nature of the eigensolutions
- 5.6.2. Normalization of the eigenvectors
- 5.6.3. Orthogonality of the eigenvectors
- 5.6.4. Relationships between the eigensolutions and damping
- 5.6.5. System matrices in terms of the eigensolutions
- 5.6.6. Eigenrelations for viscously damped systems
- 5.6.7. Numerical examples
- 5.7. Rayleigh quotient for non-viscously damped systems
- 5.8. Summary
- Chapter 6. Reduced Computational Methods for Damped Systems
- 6.1. General non-proportionally damped systems with viscous damping
- 6.1.1. Iterative approach for the eigensolutions
- 6.1.2. Summary of the algorithm
- 6.1.3. Numerical example
- 6.2. Single-degree-of-freedom non-viscously damped systems
- 6.2.1. Nonlinear eigenvalue problem for non-viscously damped systems 250
- 6.2.2. Complex conjugate eigenvalues
- 6.2.3. Real eigenvalues
- 6.2.4. Numerical examples
- 6.3. Multiple-degrees-of-freedom non-viscously damped systems
- 6.3.1. Complex conjugate eigenvalues
- 6.3.2. Real eigenvalues
- 6.3.3. Numerical example
- 6.4. Reduced second-order approach for non-viscously damped systems
- 6.4.1. Proportionally damped systems
- 6.4.2. The general case
- 6.4.3. Numerical examples
- 6.5. Summary
- Appendix
- Bibliography
- Author index
- Index.
