# Livro Noise and Vibration control Douglas D. Reynolds Engineering principles of acoustics Allyn & Bacon (1981)

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Engineering Principles ofAcoustics ^ se ana vioraiion Control DOUGLAS D. REYNOLDS A problem-solving approach to the under- standing of vibration-induced noise problems, sound wave propagation and noise control. Engineering Principles of Acoustics: Noise and Vibration Control Douglas D. Reynolds This comprehensive book gives up-to-date infornnation necessan/ to acquire an under- standing of the engineering principles asso- ciated with acoustics and noise and vibra- tion control. Complete development of equations and associated principles are pre- sented, followed by examples of their appli- cation and use. Topics included in the book are primarily related to the areas of mechan- ical vibration, generation and propagation of sound indoors and outdoors, and the control of vibration and sound propagation. Each chapter concludes with a variety of problems and possible solutions frequently encoun- tered by individuals working in the areas of architectural, industrial, and environmental noise control. Engineering Principles of Acoustics: Noise and Vibration Control also features: — chapter-by-chapter problems specified in SI units, with some conventional units, for metric measurement. — material developed and tested by the author — chapters complete with equations, illus- trations, graphs, and more to facilitate practical application. — timely and up-to-date information in light of recent federal regulations regarding noise control, the Noise Control Act of 1972. — a complete solutions manual. Digitized by the Internet Archive in 2012 http://archive.org/details/engineeringprincOOreyn Engineering Principles of Acoustics This book is a part of the ALLYN AND BACON SERIES IN MECHANICAL ENGINEERING AND APPLIED MECHANICS Consulting Editor: FRANK KREITH, University of Colorado Engineering Principles of Acoustics Noise and Vibration Control Douglas D. Reynolds ALLYN AND BACON, INC. Boston London Sydney Toronto Copyright © 1981 by Allyn and Bacon, Inc., 470 Atlantic Avenue, Boston, Massachusetts 02210. All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without written per- mission from the copyright owner. Library of Congress Cataloging in Publication Data Reynolds, Douglas D Engineering principles of acoustics. Includes bibliographical references and index. 1. Acoustical engineering. 2. Vibration. 3. Noise control. I. Title. TA365.R48 620.2 80-19098 ISBN 0-205-07271-1 ISBN (international) 0-205-07283-6 Managing Editor: Robert Roen Series Editor: David F. Pallai Production Editor: Valerie Fraser Ruud Printed in the United States of America Printing number and year (last digits): 10 9 8 7 6 5 4 3 2 1 85 84 83 82 81 80 TABLE OF CONTENTS 1. Harmonic Motion 1 1.1 Simple Harmonic Motion 1 1.2 Vectorial Representation of Harmonic Motion 1 1.3 Addition of Harmonic Signals 2 1.4 Relation between Displacement, Velocity and Accleration Signals 5 1.5 Complex Numbers 6 Problems - Chapter 1 8 2. Fundamentals of Vibration - One-Degree-of-Freedom Lumped Parameter Systems 9 2.1 Introduction 9 2.2 Constitutive Relations for Systems with Only Translational Motion 11 2.3 Constitutive Relations for Systems with Translational and Rotational Motion 13 2.4 Units 14 2.5 Equations of Motion - One-Degree-of-Freedom Systems 17 2.6 Solution to the Equation of Motion for Undamped Free Vibration 21 2.7 Solution to the Equation of Motion for Damped Free Vibration 23 2.8 Forced Vibration 27 2.9 Mechanical Impedance 32 2. 10 Power Relations 33 2.11 Force Transmitted to the Base (Transmissibil i ty) 35 2.12 Rotating and Reciprocating Unbalance 35 2.13 Comments Concerning the Magnification Factor and Transmissibi 1 i ty 42 2.14 Nomogram for Designing a Vibration Isolation System 43 2.15 Vibrating Systems Attached to Moving Supports 45 2.16 Critical Speed of a Rotating Disc on a Shaft 47 2. 17 Shock Excitation 49 2.18 Design Considerations for Simple Vibrating Systems That Are Subjected to Shock Excitation 55 2.19 General Comments Associated with Spring Elements 58 2.20 Felt and Cork Resilient Materials 62 2.21 Rubber Resilient Elements 64 2.22 Metal Springs 67 2.23 Air Springs 68 2.24 Foundation Stiffness 70 2.25 Nonviscous Damping 70 2.26 Methods for Determining the Amount of Damping in a System 75 2.27 Inertia Base for a Vibrating System 79 2.28 Recommended Criteria for Vibration Isolation of Mechanical Equipment 82 2.29 Important Symbols in Chapter 2 (not shown in Table 2.2) 86 2.30 References 86 Problems - Chapter 2 87 3. Fundamentals of Vibration - Systems with More Than One Degree of Freedom 95 3.1 Introduction 95 3.2 Equations of Motion for Mul ti-Degree-of-Freedom Systems - Newton's Method 95 3.3 Equations of Motion for Mul ti-Degree-of-Freedom Systems - Lagrange's Equation 98 3.4 Solutions to the Equations of Motion for Undamped Free Vibration 103 3.5 Solutions to the Equations of Motion for Forced Vibration 107 3.6 Dynamic Absorber 108 3.7 Vibration of a Mass with Motion in More Than One Direction 115 3.8 Semidefinite Vibration Systems 125 3.9 Influence Coefficients 127 3.10 Important Symbols in Chapter 3 138 Problems - Chapter 3 139 4. Deterministic and Random Siqnals 143 4.1 Introduction 143 4.2 Complex Periodic Signals - Complex Fourier Series 144 4.3 Complex Periodic Signals - Real Fourier Series 150 4.4 Fourier Transforms 153 4.5 Laplace Transforms 156 4.6 Inverse Laplace Transforms 161 4.7 Harmonic Response Function 167 TABLE OF CONTENTS 4.8 Convolution Integral 167 4.9 Random Signals - Mean Squared Value, Mean Value and Variance 171 4.10 Random Signals - Probability Functions 171 4.11 Measurement of Probability Density Values 175 4.12 Expected Values and Moments 178 4.13 Random Signals - Corrleation Functions 178 4.14 Measurement of Correlation Functions 182 4.15 Random Signals - Power Spectral Density Functions 184 4.16 Measurement of Power Spectral Density Functions 185 4.17 Relation between Correlation and Power Spectral Density Functions 187 4.18 Relation between Fourier Transforms and Power Spectral Density Functions 190 4.19 Important Symbols in Chapter 4 194 4.20 References 194 Problems - Chapter 4 195 5. Introduction to Wave Motion 198 5.1 Definition and Description of Wave Motion 198 5.2 General Analytical Description of Wave Motion 200 5.3 The Wave Equation ' 204 5.4 Free and Forced Waves 205 5.5 Progressive and Standing Waves 209 5.6 Important Symbols in Chapter 5 * 211 Problems - Chapter 5 212 6. Vibration of Continuous Systems 213 6.1 Introduction 213 6.2 The Wave Equation for Transverse Vibration of Strings 213 6.3 Solutions to the Wave Equation for Transverse Vibration of a String 214 6.4 Forced Vibration of a String 220 6.5 The Wave Equation for Longitudinal Vibration of a Bar 224 6.6 Solution to the Wave Equation for Longitudinal Vibration of a Bar 226 6.7 Forced Longitudinal Vibration of Bars 230 6.8 Interaction of Longitudinal Stress Waves with a Surface That Represents a Transition from One Solid Material to Another 232 6.9 The Wave Equation for Transverse Vibration of a Bar 239 6.10 Solution to the Wave Equation for Transverse Vibration of a Bar 243 6.11 The Wave Equation for Transverse Vibration of a Thin Membrane 247 6.12 Solutions to the Wave Equation for Transverse Vibration of a Thin Membrane 248 5.13 Transverse Vibration of Thin Plates 254 6.14 Important Symbols in Chapter 6 255 Problems - Chapter 6 257 7. One-Dimensional Acoustic Waves 259 7.1 Introduction 259 7.2 Continuity and Momentum Equations 259 7.3 Development of the Expression for the Wave Speed c 260 7.4