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VIBRATIONS SECOND EDITION Balakumar Balachandran | Edward B. Magrab Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Vibrations, Second Edition Balakumar Balachandran and Edward B. Magrab Director, Global Engineering Program: Chris Carson Senior Developmental Editor: Hilda Gowans Permissions: Kristiina Bowering Production Service: RPK Editorial Services, Inc. Copy Editor: Harlan James Proofreader: Martha McMaster Indexer: Shelly Gerger-Knechtl Creative Director: Angela Cluer Text Designer: RPK Editorial Services Cover Designer: Andrew Adams Cover Image: Left, © iStockphoto.com/Robert Rushton; center, © Image.com/Dreamstime.com; right, © Ben Goode/Dreamstime.com Compositor: G&S/Newgen Printer: Thomson West © 2009 Cengage Learning ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher. For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com Library of Congress Control Number: 2008925925 ISBN-13: 978-0-534-55206-0 ISBN-10: 0-534-55206-4 Cengage Learning 1120 Birchmount Road Toronto ON M1K 5G4 Canada Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at: international.cengage.com/region Cengage Learning products are represented in Canada by Nelson Education Ltd. For your course and learning solutions, visit academic.cengage.com Purchase any of our products at your local college store or at our preferred online store www.ichapters.com Printed in the United States of America 1 2 3 4 5 6 7 11 10 09 08 Contents 1 Introduction 1 1.1 Introduction 1 1.2 Preliminaries from Dynamics 4 1.3 Summary 19 Exercises 19 2 Modeling of Vibratory Systems 23 2.1 Introduction 23 2.2 Inertia Elements 24 2.3 Stiffness Elements 28 2.4 Dissipation Elements 49 2.5 Model Construction 54 2.6 Design for Vibration 60 2.7 Summary 61 Exercises 61 3 Single Degree-Of-Freedom Systems: Governing Equations 69 3.1 Introduction 69 3.2 Force-Balance and Moment-Balance Methods 70 iv Contents 3.3 Natural Frequency and Damping Factor 79 3.4 Governing Equations for Different Types of Damping 88 3.5 Governing Equations for Different Types of Applied Forces 89 3.6 Lagrange’s Equations 93 3.7 Summary 116 Exercises 117 4 Single Degree-of-Freedom System: Free-Response Characteristics 127 4.1 Introduction 127 4.2 Free Responses of Undamped and Damped Systems 129 4.3 Stability of a Single Degree-of-Freedom System 161 4.4 Machine Tool Chatter 165 4.5 Single Degree-of-Freedom Systems with Nonlinear Elements 168 4.6 Summary 174 Exercises 174 5 Single Degree-of-Freedom Systems Subjected to Periodic Excitations 181 5.1 Introduction 181 5.2 Response to Harmonic Excitation 183 5.3 Frequency-Response Function 204 5.4 System with Rotating Unbalanced Mass 218 5.5 System with Base Excitation 225 5.6 Acceleration Measurement: Accelerometer 235 5.7 Vibration Isolation 238 ... - tailieumienphi.vn
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