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Cover; Title Page; Contents; Preface; Nomenclature; Chapter 1. Parametric Sensitivity of Damped Systems; 1.1. Parametric sensitivity of undamped systems; 1.1.1. Sensitivity of the eigenvalues; 1.1.2. Sensitivity of the eigenvectors; 1.2. Parametric sensitivity of viscously damped systems; 1.2.1. Sensitivity of the eigenvalues; 1.2.2. Sensitivity of the eigenvectors; 1.3. Parametric sensitivity of non-viscously damped systems; 1.3.1. Sensitivity of the eigenvalues; 1.3.2. Sensitivity of the eigenvectors; 1.4. Summary; Chapter 2. Identification of Viscous Damping
2.1. Identification of proportional viscous damping 2.1.1. Damping identification using generalized proportional damping; 2.1.2. Error propagation in the damping identification method; 2.1.3. Numerical examples; 2.1.4. Experimental results; 2.1.5. Synopsis; 2.2. Identification of non-proportional viscous damping; 2.2.1. The theory of damping identification; 2.2.2. Numerical examples; 2.2.3. Error analysis; 2.2.4. Synopsis; 2.3. Symmetry-preserving damping identification; 2.3.1. The theory of symmetric damping matrix identification; 2.3.2. Numerical examples; 2.3.3. Synopsis
2.4. Direct identification of the damping matrix 2.4.1. The modified Lancaster's method; 2.4.2. Numerical examples; 2.4.3. Synopsis; 2.5. Summary; Chapter 3. Identification of Non-viscous Damping; 3.1. Identification of exponential non-viscous damping model; 3.1.1. Background of complex modes; 3.1.2. Fitting of the relaxation parameter; 3.1.3. Fitting of the coefficient matrix; 3.1.4. Synopsis; 3.2. Symmetry preserving non-viscous damping identification; 3.2.1. Theory; 3.2.2. Numerical examples; 3.2.3. Synopsis; 3.3. Direct identification of non-viscous damping
3.3.1. Lancaster's method for non-viscously damped systems 3.3.2. Numerical examples; 3.3.3. Synopsis; 3.4. Summary; Chapter 4. Quantification of Damping; 4.1. Quantification of non-proportional damping; 4.1.1. Optimal normalization of complex modes; 4.1.2. An index of non-proportionality; 4.1.3. Alternative normalization methods; 4.1.4. Synopsis; 4.2. Quantification of non-viscous damping; 4.2.1. Non-viscosity indices; 4.2.2. Numerical examples; 4.2.3. Error analysis; 4.2.4. Synopsis; 4.3. Summary; Bibliography; Author Index; Index
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 bo