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:
Analysis, 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:
parametric senistivity of damped systems; identification of viscous
damping; identification of non-viscous damping; and some tools for
the quanitification of damping. 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. Parametric Sensitivity of Damped Systems.
2. Identification of Viscous Damping.
3. Identification of Non-viscous Damping.
4. Quantification of Damping.
About the Authors
Sondipon Adhikari is Chair Professor of Aerospace Engineering at
Swansea University, Wales. His wide-ranging and multi-disciplinary
research interests include uncertainty quantification in
computational mechanics, bio- and nanomechanics, dynamics of
complex systems, inverse problems for linear and nonlinear
dynamics, and renewable energy. He is a technical reviewer of 97
international journals, 18 conferences and 13 funding bodies.He has
written over 180 refereed journal papers, 120 refereed conference
papers and has authored or co-authored 15 book chapters.
Spis treści
Preface ix
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 Lancaster’s 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. Lancaster’s 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
O autorze
Sara J. Wilkinson is Associate Professor of Property and
Construction at the University of
Technology, Sydney, Australia
Hilde Remøy is Assistant Professor of Real Estate
Management at Delft University of
Technology, The Netherlands
Craig Langston is Professor of Construction and Facilities
Management at Bond University,
Queensland, Australia
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