Table of Contents
Introduction and Background
Basic Concepts of Systems and Structures
Basic Concepts of Vibration
Basic Concepts of Random Vibration
Types of System Models
Basic Dynamics
Units
Concluding Summary
Single Degree-of-Freedom Vibration: Discrete Models
Motivating Examples
Mathematical Modeling: Deterministic
Undamped Free Vibration
Harmonic Forcing with no Damping
Concepts Summary
Single Degree-of-Freedom Vibration: Discrete Models with Damping
Damping
Free Vibration with Viscous Damping
Free Response with Coulomb Damping
Forced Vibration with Viscous Damping
Forced Harmonic Vibration
Periodic but Not Harmonic Excitation
Concepts Summary
Single Degree-of-Freedom Vibration: General Loading and Advanced Topics
Arbitrary Loading: Laplace Transform
Step Loading
Impulsive Excitation
Arbitrary Loading
Introduction to Lagrange.s Equation
Notions of Randomness
Notions of Control
The Inverse Problem
A Self-Excited System and its Stability
Solution Analysis and Design Techniques
A Model of a Bouncing Ball
Concepts Summary
Single Degree-of-Freedom Vibration: Probabilistic Forces
Introduction
Example Problems and Motivation
Random Variables
Mathematical Expectation
Useful Probability Densities
Two Random Variables
Random Processes
Random Vibration
Concepts Summary
Vibration Control
Motivation
Approaches to Controlling Vibration
Feedback Control
Performance of Feedback Control Systems
Control of Response
Sensitivity to Parameter Variations
State Variable Models
Concepts Summary
Variational Principles and Analytical Dynamics
Introduction
Virtual Work
Lagrange.s Equation of Motion
Hamilton’s Principle
Lagrange’s Equation with Damping
Concepts Summary
Multi Degree-of-Freedom Vibration: Introductory Topics
Example Problems and Motivation
The Concepts of Stiffness and Flexibility
Derivation of Equations of Motion
Undamped Vibration
Direct Method: Free Vibration with Damping
Modal Analysis
Real and Complex Modes
Concepts Summary
Multi Degree-of-Freedom Vibration: Advanced Topics
Overview
Unrestrained Systems
The Geometry of the Eigenvalue Problem
Periodic Structures
Inverse Vibration
Sloshing of Fluids in Containers
Stability of Motion
Multivariable Control
MDOF Stochastic Response
Stochastic Control
Rayleigh.s Quotient
Monte Carlo Simulation
Concepts Summary
Continuous Models for Vibration
Continuous Limit of a Discrete Formulation
Vibration of String
Longitudinal (Axial) Vibration of Beams
Torsional Vibration of Shafts
10.5 Transverse Vibration of Beams
10.6 Beam Vibration: Special Problems
Concepts Summary
Continuous Models for Vibration: Advanced Models
Vibration of Membranes
Vibration of Plates
Random Vibration of Continuous Structures
Approximate Methods
Variables That Do Not Separate
Concepts Summary
Nonlinear Vibration
Examples of Nonlinear Vibration
The Phase Plane
Perturbation Methods
The Mathieu Equation
The van der Pol Equation
Motion in the Large
Nonlinear Control
Advanced Topics
Concluding Summary
Appendices
A Mathematical Concepts for Vibration
Complex Numbers
Matrices
Taylor Series and Linearization
Ordinary Differential Equations
Laplace Transforms
Fourier Series and Transforms
Partial Differential Equations
Index