Vibrations

by Balachandran, Balakumar; Magrab, Edward B.

• ISBN13: 9780534552060
• ISBN10: 0534552064
• Edition: 2nd
• Format: Hardcover
• Copyright: 2008-05-26
• Publisher: CL Engineering

Summary

Featuring outstanding coverage of linear and non-linear single degree-of-freedom and multi-degree-of-freedom systems, this book teaches the use of vibration principles in a broad spectrum of applications. In this introduction for undergraduate students, authors Balakumar Balachandran and Edward B. Magrab present vibration principles in a general context and illustrate the use of these principles through carefully chosen examples from different disciplines. Their balanced approach integrates principles of linear and nonlinear vibrations with modeling, analysis, prediction, and measurement so that physical understanding of the vibratory phenomena and their relevance for engineering design can be emphasized. The authors also provide design guidelines that are applicable to a wide range of vibratory systems. MATLAB is thoroughly integrated throughout the text.

Table of Contents

Introduction

Introduction

Preliminaries from Dynamics

Summary

Exercises

Modeling of Vibratory Systems

Introduction

Inertia Elements

Stiffness Elements

Dissipation Elements

Model Construction

Design for Vibration

Summary

Exercises

Single Degree-of-Freedom Systems: Governing Equations

Introduction

Force-Balance and Moment-Balance Methods

Natural Frequency and Damping Factor

Governing Equations for Different Types of Damping

Governing Equations for Different Types of Applied Forces

Lagranges Equations

Summary

Exercises

Single Degree-of-Freedom System: Solution for Response and Free-Response Characteristics

Introduction

Free Responses of Undamped and Damped Systems

Stability of Single Degree-of-Freedom System

Machine Tool Chatter

Single Degree-of-Freedom Systems with Nonlinear Elements

Summary

Exercises

Single Degree-of-Freedom Systems Subjected to Periodic Excitations

Introduction

Response to Harmonic Excitation

Frequency-Response Function

Systems with Rotating Unbalanced Mass

Systems with Base Excitation

Acceleration Measurement: Accelerometer

Vibration Isolation

Energy Dissipation and Equivalent Damping

Response to Excitation with Harmonic Components

Influence of Nonlinear Stiffness on Forced Response

Summary

Exercises

Single Degree-of-Freedom Systems Subjected to Transient Excitations

Introduction

Response to Impulse Excitation

Response to Step Input

Response to Ramp Input

Spectral Energy of the Response

Response to Rectangular Pulse Excitation

Response to Half-Sine Wave Pulse

Impact Testing

Summary

Exercises

Multiple Degree-of-Freedom Systems: Governing Equations and Natural Frequencies and Mode Shapes

Introduction

Governing Equations

Free Responses

Rotating Shafts on Flexible Supports

Stability

Summary

Exercises

Multiple Degree-of-Freedom Systems: General Solution for Response and Forced Oscillations

Introduction

Normal-Mode Approach

State-Space Formulation

Laplace Transform Approach

Transfer Functions and Frequency-Response Functions

Vibration Absorbers

Vibration Isolation: Transmissibility Ratio

Systems with Moving Base

Summary

Exercises

Vibrations of Beams

Introduction

Governing Equations of Motion

Free Oscillations: Natural Frequencies and Mode Shapes

Forced Oscillations

Summary

Glossary

Appendix

Laplace Transform Pairs

Fourier Series

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