Mechanical Vibration: Analysis, Uncertainties, and Control 3rd Edition

Mechanical Vibration: Analysis, Uncertainties, and Controlsimply and comprehensively addresses the fundamental principles of vibration theory, emphasizing its application in solving practical engineering problems. The authors focus on strengthening engineers’ command of mathematics as a cornerstone for understanding vibration, control, and the ways in which uncertainties affect analysis. It provides a detailed exploration and explanation of the essential equations involved in modeling vibrating systems and shows readers how to employ MATLAB® as an advanced tool for analyzing specific problems.

Forgoing the extensive and in-depth analysis of randomness and control found in more specialized texts, this straightforward, easy-to-follow volume presents the format, content, and depth of description that the authors themselves would have found useful when they first learned the subject. The authors assume that the readers have a basic knowledge of dynamics, mechanics of materials, differential equations, and some knowledge of matrix algebra. Clarifying necessary mathematics, they present formulations and explanations to convey significant details.

The material is organized to afford great flexibility regarding course level, content, and usefulness in self-study for practicing engineers or as a text for graduate engineering students. This work includes example problems and explanatory figures, biographies of renowned contributors, and access to a website providing supplementary resources. These include an online MATLAB primer featuring original programs that can be used to solve complex problems and test solutions.

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 withDamping

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 Sti¤ness 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 Di¤erential Equations

Laplace Transforms

Fourier Series and Transforms

Partial Di¤erential Equations

Index

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