Structural Dynamic Analysis with Generalized Damping Models

Nomenclature  xiii

Chapter 1. Parametric Sensitivity of Damped Systems  1

1.1. Parametric sensitivity of undamped systems   2

1.1.1. Sensitivity of the eigenvalues 2

1.1.2. Sensitivity of the eigenvectors    3

1.2. Parametric sensitivity of viscously damped systems 5

1.2.1. Sensitivity of the eigenvalues 6

1.2.2. Sensitivity of the eigenvectors    9

1.3. Parametric sensitivity of non-viscously damped systems 22

1.3.1. Sensitivity of the eigenvalues 23

1.3.2. Sensitivity of the eigenvectors    25

1.4. Summary   41

Chapter 2. Identification of Viscous Damping 43

2.1. Identification of proportional viscous damping   44

2.1.1. Damping identification using generalized proportional damping  45

2.1.2. Error propagation in the damping identification method   48

2.1.3. Numerical examples 49

2.1.4. Experimental results 51

2.1.5. Synopsis  67

2.2. Identification of non-proportional viscous damping 69

2.2.1. The theory of damping identification 71

2.2.2. Numerical examples 75

2.2.3. Error analysis 88

2.2.4. Synopsis  90

2.3. Symmetry-preserving damping identification 91

2.3.1. The theory of symmetric damping matrix identification   91

2.3.2. Numerical examples 97

2.3.3. Synopsis  104

2.4. Direct identification of the damping matrix   104

2.4.1. The modified Lancasterâs method 105

2.4.2. Numerical examples 111

2.4.3. Synopsis  117

2.5. Summary   118

Chapter 3. Identification of Non-viscous Damping 121

3.1. Identification of exponential non-viscous damping model   123

3.1.1. Background of complex modes    123

3.1.2. Fitting of the relaxation parameter 125

3.1.3. Fitting of the coefficient matrix    140

3.1.4. Synopsis  149

3.2. Symmetry preserving non-viscous damping identification   151

3.2.1. Theory 151

3.2.2. Numerical examples 155

3.2.3. Synopsis  159

3.3. Direct identification of non-viscous damping 160

3.3.1. Lancasterâs method for non-viscously damped systems   161

3.3.2. Numerical examples 165

3.3.3. Synopsis  167

3.4. Summary   168

Chapter 4. Quantification of Damping  169

4.1. Quantification of non-proportional damping   169

4.1.1. Optimal normalization of complex modes   171

4.1.2. An index of non-proportionality 182

4.1.3. Alternative normalization methods 187

4.1.4. Synopsis  193

4.2. Quantification of non-viscous damping 193

4.2.1. Non-viscosity indices 195

4.2.2. Numerical examples 203

4.2.3. Error analysis  208

4.2.4. Synopsis  211

4.3. Summary   211

Bibliography 213

Author Index 243

Index 245