Damping Models for Structural Vibration
File : pdf, 3.9MB, 228 pages
PhD Thesis by Adhikari Sondipon
TOC
1 Introduction
1.1 Dynamics of Undamped Systems
1.1.1 Equation of Motion
1.1.2 Modal Analysis
1.2 Models of Damping
1.2.1 Single Degree-of-freedom Systems
1.2.2 Continuous Systems
1.2.3 Multiple Degrees-of-freedom Systems
1.2.4 Other Studies
1.3 Modal Analysis of Viscously Damped Systems
1.3.1 The State-Space Method
1.3.2 Methods in Configuration Space
1.4 Analysis of Non-viscously Damped Systems
1.5 Identification of Viscous Damping
1.5.1 Single Degree-of-freedom Systems Systems
1.5.2 Multiple Degrees-of-freedom Systems
1.6 Identification of Non-viscous Damping
1.7 Open Problems
1.8 Outline of the Dissertation
2 The Nature of Proportional Damping
2.1 Introduction
2.2 Viscously Damped Systems
2.2.1 Existence of Classical Normal Modes
2.2.2 Generalization of Proportional Damping
2.3 Non-viscously Damped Systems
2.3.1 Existence of Classical Normal Modes
2.3.2 Generalization of Proportional Damping
2.4 Conclusions
3 Dynamics of Non-viscously Damped Systems
3.1 Introduction
3.2 Eigenvalues and Eigenvectors
3.2.1 Elastic Modes
3.2.2 Non-viscous Modes
3.2.3 Approximations and Special Cases
3.3 Transfer Function
3.3.1 Eigenvectors of the Dynamic Stiffness Matrix
3.3.2 Calculation of the Residues
3.3.3 Special Cases
3.4 Dynamic Response
3.5 Summary of the Method
3.6 Numerical Examples
3.7 The System
3.7.1 Example 1: Exponential Damping
3.7.2 Example 2: GHM Damping
3.8 Conclusions
4 Some General Properties of the Eigenvectors
4.1 Introduction
4.2 Nature of the Eigensolutions
4.3 Normalization of the Eigenvectors
4.4 Orthogonality of the Eigenvectors
4.5 Relationships Between the Eigensolutions and Damping
4.5.1 Relationships in Terms of M-1
4.5.2 Relationships in Terms of K-1
4.6 System Matrices in Terms of the Eigensolutions
4.7 Eigenrelations for Viscously Damped Systems
4.8 Numerical Examples
4.8.1 The System
4.8.2 Eigenvalues and Eigenvectors
4.8.3 Orthogonality Relationships
4.8.4 Relationships With the Damping Matrix
4.9 Conclusions
5 Identification of Viscous Damping
5.1 Introduction
5.2 Background of Complex Modes
5.3 Identification of Viscous Damping Matrix
5.4 Numerical Examples
5.4.1 Results for Small
5.4.2 Results for Larger
5.5 Conclusions
6 Identification of Non-viscous Damping
6.1 Introduction
6.2 Background of Complex Modes
6.3 Fitting of the Relaxation Parameter
6.3.1 Theory
6.3.2 Simulation Method
6.3.3 Numerical Results
6.4 Selecting the Value of
6.4.1 Discussion
6.5 Fitting of the Coefficient Matrix
6.5.1 Theory
6.5.2 Summary of the Identification Method
6.5.3 Numerical Results
6.6 Conclusions
7 Symmetry Preserving Methods
7.1 Introduction
7.2 Identification of Viscous Damping Matrix
7.2.1 Theory
7.2.2 Numerical Examples
7.3 Identification of Non-viscous Damping
7.3.1 Theory
7.3.2 Numerical Examples
7.4 Conclusions
8 Experimental Identification of Damping
8.1 Introduction
8.2 Extraction of Modal Parameters
8.2.1 Linear Least-Square Method
8.2.2 Determination of the Residues
8.2.3 Non-linear Least-Square Method
8.2.4 Summary of the Method
8.3 The Beam Experiment
8.3.1 Experimental Set-up
8.3.2 Experimental Procedure
8.4 Beam Theory
8.5 Results and Discussions
8.5.1 Measured and Fitted Transfer Functions
8.5.2 Modal Data
8.5.3 Identification of the Damping Properties
8.6 Error Analysis
8.6.1 Error Analysis for Viscous Damping Identification
8.6.2 Error Analysis for Non-viscous Damping Identification
8.7 Conclusions
9 Summary and Conclusions
9.1 Summary of the Contributions Made
9.2 Suggestions for Further Work
A Calculation of the Gradient and Hessian of the Merit Function
B Discretized Mass Matrix of the Beam
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