Engineering principles of acoustics: Noise and vibration control

664 Pages·1981·47.42 MB·English

by  Douglas D. Reynolds

Engineering Principles
of Acoustics
^ se ana vioraiion Control
DOUGLAS REYNOLDS
D.
A problem-solving approach to the under-
standing of vibration-induced noise problems,
sound wave propagation and noise control.
Engineering Principles ofAcoustics:
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 theirappli-
cation and use. Topics included in the book
are primarily related tothe areas of mechan-
ical vibration, generation and propagation of
sound indoors and outdoors, and the control
of vibration and sound propagation. Each
chapterconcludeswith a variety of problems
and possible solutions frequentlyencoun-
tered by individualsworking in the areas of
architectural, industrial, and environmental
noise control.
Engineering Principles ofAcoustics:
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 completewith 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
2012
in
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 ofAmerica
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 (Transmissibility) 35
2.12 Rotating and Reciprocating Unbalance 35
2.13 Comments Concerning the Magnification Factor and Transmissibi1ity 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 Multi-Degree-of-Freedom Systems - Newton's Method 95
3.3 Equations of Motion for Multi-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 forTransverse 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 Development of the Wave Equation for the Propagation of Sound in Air 262
7.5 Other Variables Associated with Plane Acoustic Waves 263
7.6 Solutions to the Wave Equation for the Propagation of Plane Waves in Air 264
7.7 One-Dimensional Spherical Waves 270
7.8 Radiation Fields of a Spherical Sound Source 271
7.9 Root Mean Spuare Value of a Parameter 272
7.10 Acoustic Intensity 273
^7.11 Sound Energy Density 274
-f-\j.\2 Sound Power 275
7.13 Levels 277
7.14 Additive Effects of Sound Sources 280
7.15 The Effects of Reflecting Surfaces on a Sound Source 283
7.16 Weighted Levels, Band Levels and Spectrum Levels 284
7.17 Important Symbols in Chapter 7 288
7.18 References 288
Problems - Chapter 7 289
8. Acoustic Transmission Phenomena 292
8.1 Introduction 292
8.2 Sound Transmission from One Medium to Another (Normal Incidence) 292
Sound transmission from One Medium to Another (Oblique Incidence) 295
Interaction of a Plane Acoustic Wave with a Normally Reacting Solid (Oblique Incidence) 298
The Use of an Impedance Tube to Measure the Sound Power Absorption Coefficient and Specific
Acoustic Impedance of a Normally Reacting Solid ^ 299
Sound Transmission through a Solid Barrier Using the Concept of Layered Media 303
Transmission of Plane Waves through a Thin Massive Panel (Oblique Incidence) 304