Dynamics of Very High Dimensional Systems

Earl H Dowell, Deman Tang;;;

• Publisher: WSPC
• Year: 2003
• eBook ISBN: 9789813102279
• Topic: Technology & Engineering
• Subtopic: Aeronautic & Astronautic Engineering
• Index: Technology & Engineering

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

• Contents
• Preface
• 1 Introduction
• 2 Linear and Nonlinear Dynamics of the String - A Prototypical Example
• 3 Equations of Motion for a Nonlinear Beam with Tension (String with Bending Stiffness)
• 4 Convergence of a Modal Series
• 5 Self-Adjoint versus Non-Self-Adjoint (or Conservative versus Non-Conservative) Systems
• 6 Orthogonality
• 7 Nonlinear Normal Modes ("Eigenmodes")
• 8 Derivation of Lagrange's Equations from Hamilton's Principle Including the Effects of Constraints
• 9 Normal Forms for Kinetic and Potential Energy
• 10 Component Modal Analysis
• 11 Asymptotic Modal Analysis (AMA)
• 12 Modeling of Acoustic-Structural Interaction: Acoustoelasticity
• 13 Modeling of Fluid-Structural Interaction: Aeroelasticity
• 14 Nonlinear Aeroelasticity
• 15 Reduced-Order Model Analysis For Nanoscale Systems
• 16 General Bibliography
• Epilogue
• Index