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9789812384676

Dynamics of Very High Dimensional Systems

by ;
  • ISBN13:

    9789812384676

  • ISBN10:

    9812384677

  • Format: Paperback
  • Copyright: 2003-08-01
  • Publisher: World Scientific Pub Co Inc
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Supplemental Materials

What is included with this book?

Summary

Many books on dynamics start with a discussion of systems with one or two degrees of freedom and then turn to the generalization to the case of many degrees of freedom. For linear systems, the concept of eigenfunctions provides a compact and elegant method for decomposing the dynamics of a high dimensional system into a series of independent single-degree-of-freedom dynamical systems. Yet, when the system has a very high dimension, the determination of the eigenfunctions may be a distinct challenge, and when the dynamical system is nonconservative and/or nonlinear, the whole notion of uncoupled eigenmodes requires nontrivial extensions of classical methods. These issues constitute the subject of this book.

Table of Contents

Preface v
1 Introduction
1(4)
2 Linear and Nonlinear Dynamics of the String - A Prototypical Example
5(10)
2.1 Fluid Analogs: Acoustic Oscillations
12(1)
2.2 Generalizations to Higher Spatial Dimensions
13(2)
3 Equations of Motion for a Nonlinear Beam with Tension (String with Bending Stiffness)
15(4)
4 Convergence of a Modal Series
19(4)
5 Self-Adjoint versus Non-Self-Adjoint (or Conservative versus Non-Conservative) Systems
23(10)
5.1 Eigenvalues and Eigenvectors
23(5)
5.2 Proper Orthogonal Decomposition
28(3)
5.3 Second Order (in Time Differentiation) Nonlinear Systems
31(2)
6 Orthogonality
33(6)
6.1 Continuous Systems
33(3)
6.2 Discrete Systems
36(3)
7 Nonlinear Normal Modes ( "Eigenmodes" )
39(10)
7.1 A (Relatively) Simple Example for a Two Degree of Freedom System (Four First Order Equations)
41(3)
7.2 Adding More Degrees of Freedom
44(1)
7.3 Adding External Excitation
45(2)
7.4 References
47(2)
8 Derivation of Lagrange's Equations from Hamilton's Principle Including the Effects of Constraints
49(6)
9 Normal Forms for Kinetic and Potential Energy
55(4)
10 Component Modal Analysis 59(16)
10.1 An Example
61(3)
10.2 Nonlinear Systems
64(3)
10.3 Damping
67(3)
10.4 Eigenmodes
70(1)
10.5 Another Example
70(2)
10.6 References
72(3)
11 Asymptotic Modal Analysis (AMA) 75(18)
11.1 Classical Modal Analysis with Random Excitation
76(1)
11.2 Correlation Functions, Power Spectra and Mean Squares
76(1)
11.3 Point Forces
77(1)
11.4 Computation of the Mean Square Response
78(1)
11.5 The "White Noise", Small Damping Approximation
79(1)
11.6 The Asymptotic Limit of Classical Modal Analysis
80(4)
11.7 Comparison of Results from Asymptotic Modal Analysis (AMA) with those from Classical Modal Analysis (CMA) and Experiment
84(3)
11.8 References
87(6)
12 Modeling of Acoustic-Structural Interaction: Acoustoelasticity 93(38)
12.1 Introduction
93(1)
12.2 Coupled Fluid-Structural Motion of an Acoustic Cavity with a Flexible and/or Absorbing Wall: General Theory
94(7)
12.2.1 Acoustical Problem
94(3)
12.2.2 Structural Modal Expansion
97(1)
12.2.3 Structural Considerations
98(2)
12.2.4 A Variational Formulation
100(1)
12.3 Acoustic Natural Modes in Multiply Connected Cavities
101(4)
12.4 Numerical Results for Acoustic Modes and Comparisons with Experiments
105(3)
12.4.1 Acoustic Natural Modes in Multiply Connected Cavities
105(3)
12.5 Forced Response of a Cavity with a Flexible and/or Absorbing Wall
108(11)
12.5.1 Basic Model
108(3)
12.5.2 Simplified Model
111(8)
12.6 Numerical Results for Forced Response of a Single Cavity with a Flexible Wall and Comparisons with Experiment
119(4)
12.6.1 Experimental Arrangemënt
119(1)
12.6.2 Cavity Pressure Measurement
119(2)
12.6.3 Effect of Cavity on Panel Resonant Frequency
121(1)
12.6.4 Panel Damping
121(1)
12.6.5 Cavity Pressure and Damping Effects
122(1)
12.7 Concluding Remarks
123(1)
12.8 References
124(3)
12.9 Appendix 1: Further Data on the Experimental Apparatus of Section 12.6
127(2)
12.9.1 Plate (in Vacuo) Modes
127(1)
12.9.2 Cavity (Rigid Wall) Modes
127(2)
12.9.3 Change in Wall Mode Shapes with Cavity Depth
129(1)
12.10 Appendix 2: List of Symbols
129(2)
13 Modeling of Fluid-Structural Interaction: Aeroelasticity 131(54)
13.1 Introduction
131(1)
13.2 The Range of Physical Models
132(5)
13.2.1 The Classical Models
132(3)
13.2.2 The Distinction Between Linear and Nonlinear Models
135(1)
13.2.3 Computational Fluid Dynamics Models
136(1)
13.2.4 The Computational Challenge of Fluid Structure Interaction Modeling
136(1)
13.3 Time-Linearized Models
137(4)
13.3.1 Classical Aerodynamic Theory
137(1)
13.3.2 Classical Hydrodynamic Stability Theory
138(1)
13.3.3 Parallel Shear Flow with an Inviscid Dynamic Perturbation
139(1)
13.3.4 General Time-Linearized Analysis
139(2)
13.3.5 Some Numerical Examples
141(1)
13.4 Nonlinear Dynamical Models
141(5)
13.4.1 Harmonic Balance Method
144(1)
13.4.2 System Identification Methods
145(1)
13.4.3 Nonlinear Reduced-Order Models
145(1)
13.5 Reduced-Order Models
146(29)
13.5.1 Constructing Reduced-Order Models
147(1)
13.5.2 Linear and Nonlinear Fluid Models
148(1)
13.5.3 Eigenmode Computational Methodology
149(1)
13.5.4 Proper Orthogonal Decomposition Modes
149(2)
13.5.5 Balanced Modes
151(1)
13.5.6 Synergy Among the Modal Methods
151(1)
13.5.7 Input/Output Models
152(1)
13.5.8 Structural, Aerodynamic, and Aeroelastic Modes
153(2)
13.5.9 Representative Results
155(1)
13.5.10 The Effects of Spatial Discretization and a Finite Computational Domain
155(3)
13.5.11 The Effects of Mach Number and Steady Angle of Attack; Subsonic and Transonic Flows
158(8)
13.5.12 The Effects of Viscosity
166(1)
13.5.13 Nonlinear Aeroelastic Reduced-Order Models
167(8)
13.6 Concluding Remarks and Directions for Future Research
175(1)
13.7 References
176(5)
13.8 Appendix: Singular-Value Decomposition, Proper Orthogonal Decomposition, and Balanced Modes
181(4)
14 Nonlinear Aeroelasticity 185(36)
14.1 Introduction
185(1)
14.2 Scope of This Chapter
186(19)
14.2.1 Airfoil Plus a Control Surface with Freeplay
188(8)
14.2.2 Low Aspect Ratio, Plate-Like Wing
196(2)
14.2.3 High Aspect Ratio, Beam-Like Wing
198(2)
14.2.4 Nonlinear Inviscid Aerodynamic Effects on Transonic Divergence Flutter and Limit Cycle Oscillations
200(5)
14.3 Concluding Remarks
205(2)
14.4 Future Work
207(2)
14.5 References
209(5)
14.6 Appendix 1: Modeling for Nonlinear Aeroelastic Analysis
214(5)
14.6.1 Modeling of the Structure
215(1)
14.6.2 Modeling of the Fluid
216(1)
14.6.3 Solving the Aeroelastic Equations
217(2)
14.7 Appendix 2: List of Symbols
219(2)
15 Reduced-Order Model Analysis For Nanoscale Systems 221(44)
15.1 Introduction
221(3)
15.2 Theoretical Model
224(9)
15.2.1 Static Equilibrium Position
227(2)
15.2.2 Small Dynamic Pertebations
229(1)
15.2.3 Reduced-Order (Dynamic) Model
230(3)
15.3 Numerical Analysis
233(26)
15.3.1 Results for I =100
234(14)
15.3.2 Results for I =1000
248(11)
15.4 Concluding Remarks
259(1)
15.5 References
260(1)
15.6 Appendix A: Dynamic Perturbation Variables
261(1)
15.7 Appendix B: Derivation of Dynamic Perturbation Equations
262(3)
16 General Bibliography 265(2)
Epilogue 267(2)
Index 269

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