Fundamentals of Noise and Vibration Analysis for Engineers Noiseandvibrationaffectsallkindsofengineeringstructures,andisfastbecominganintegralpart ofengineeringcoursesatuniversitiesandcollegesaroundtheworld.Inthissecondedition,Michael Norton’sclassictexthasbeenextensivelyupdatedtotakeintoaccountrecentdevelopmentsinthe field.MuchofthenewmaterialhasbeenprovidedbyDenisKarczub,whojoinsMichaelassecond authorforthisedition. Thisbooktreatsbothnoiseandvibrationinasinglevolume,withparticularemphasisonwave– modedualityandinteractionsbetweensoundwavesandsolidstructures.Therearenumerouscase studies,testcasesandexamplesforstudentstoworkthrough.Thebookisprimarilyintendedasa textbookforseniorlevelundergraduateandgraduatecourses,butisalsoavaluablereferencefor practitionersandresearchersinthefieldofnoiseandvibration. Fundamentals of Noise and Vibration Analysis for Engineers Second edition M. P. Norton SchoolofMechanicalEngineering,UniversityofWesternAustralia and D. G. Karczub S.V.T.EngineeringConsultants,Perth,WesternAustralia CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521495616 © First edition Cambridge University Press 1989 © Second edition M. P. Norton and D. G. Karczub 2003 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First edition published 1989 Reprinted 1994 Second edition published 2003 A catalogue record for this publication is available from the British Library ISBN 978-0-521-49561-6 hardback ISBN 978-0-521-49913-2 paperback Transferred to digital printing 2007 To ourparents, thefirstauthor’swifeErica, andhisyoungdaughtersCaitlinandSarah Contents Preface pagexv Acknowledgements xvii Introductorycomments xviii 1 Mechanical vibrations: a review of some fundamentals 1 1.1 Introduction 1 1.2 Introductorywavemotionconcepts–anelasticcontinuumviewpoint 3 1.3 Introductorymultiple,discrete,mass–spring–damperoscillatorconcepts– amacroscopicviewpoint 8 1.4 Introductoryconceptsonnaturalfrequencies,modesofvibration,forced vibrationsandresonance 10 1.5 Thedynamicsofasingleoscillator–aconvenientmodel 12 1.5.1 Undampedfreevibrations 12 1.5.2 Energyconcepts 15 1.5.3 Freevibrationswithviscousdamping 16 1.5.4 Forcedvibrations:somegeneralcomments 21 1.5.5 Forcedvibrationswithharmonicexcitation 22 1.5.6 Equivalentviscous-dampingconcepts–dampinginrealsystems 30 1.5.7 Forcedvibrationswithperiodicexcitation 32 1.5.8 Forcedvibrationswithtransientexcitation 33 1.6 Forcedvibrationswithrandomexcitation 37 1.6.1 Probabilityfunctions 38 1.6.2 Correlationfunctions 39 1.6.3 Spectraldensityfunctions 41 1.6.4 Input–outputrelationshipsforlinearsystems 42 1.6.5 Thespecialcaseofbroadbandexcitationofasingleoscillator 50 1.6.6 Anoteonfrequencyresponsefunctionsandtransferfunctions 52 1.7 Energyandpowerflowrelationships 52 vii viii Contents 1.8 Multipleoscillators–areviewofsomegeneralprocedures 56 1.8.1 Asimpletwo-degree-of-freedomsystem 56 1.8.2 Asimplethree-degree-of-freedomsystem 59 1.8.3 Forcedvibrationsofmultipleoscillators 60 1.9 Continuoussystems–areviewofwave-typesinstrings,barsandplates 64 1.9.1 Thevibratingstring 64 1.9.2 Quasi-longitudinalvibrationsofrodsandbars 72 1.9.3 Transmissionandreflectionofquasi-longitudinalwaves 77 1.9.4 Transversebendingvibrationsofbeams 79 1.9.5 Ageneraldiscussiononwave-typesinstructures 84 1.9.6 Modesummationprocedures 85 1.9.7 Theresponseofcontinuoussystemstorandomloads 91 1.9.8 Bendingwavesinplates 94 1.10 Relationshipsfortheanalysisofdynamicstressinbeams 96 1.10.1 Dynamicstressresponseforflexuralvibrationofathinbeam 96 1.10.2 Far-fieldrelationshipsbetweendynamicstressandstructural vibrationlevels 100 1.10.3 Generalisedrelationshipsforthepredictionofmaximum dynamicstress 102 1.10.4 Propertiesofthenon-dimensionalcorrelationratio 103 1.10.5 Estimatesofdynamicstressbasedonstaticstressand displacement 104 1.10.6 Mean-squareestimatesforsingle-modevibration 105 1.10.7 Relationshipsforabase-excitedcantileverwithtipmass 106 1.11 Relationshipsfortheanalysisofdynamicstraininplates 108 1.11.1 Dynamicstrainresponseforflexuralvibrationofaconstrained rectangularplate 109 1.11.2 Far-fieldrelationshipsbetweendynamicstressandstructural vibrationlevels 112 1.11.3 Generalisedrelationshipsforthepredictionofmaximum dynamicstress 113 1.12 Relationshipsfortheanalysisofdynamicstrainincylindricalshells 113 1.12.1 Dynamicresponseofcylindricalshells 114 1.12.2 Propagatingandevanescentwavecomponents 117 1.12.3 Dynamicstrainconcentrationfactors 119 1.12.4 Correlationsbetweendynamicstrainandvelocityspatial maxima 119 References 122 Nomenclature 123 ix Contents 2 Sound waves: a review of some fundamentals 128 2.1 Introduction 128 2.2 Thehomogeneousacousticwaveequation–aclassicalanalysis 131 2.2.1 Conservationofmass 134 2.2.2 Conservationofmomentum 136 2.2.3 Thethermodynamicequationofstate 139 2.2.4 Thelinearisedacousticwaveequation 140 2.2.5 Theacousticvelocitypotential 141 2.2.6 Thepropagationofplanesoundwaves 143 2.2.7 Soundintensity,energydensityandsoundpower 144 2.3 Fundamentalacousticsourcemodels 146 2.3.1 Monopoles–simplesphericalsoundwaves 147 2.3.2 Dipoles 151 2.3.3 Monopolesneararigid,reflecting,groundplane 155 2.3.4 Soundradiationfromavibratingpistonmountedinarigidbaffle 157 2.3.5 Quadrupoles–lateralandlongitudinal 162 2.3.6 Cylindricallinesoundsources 164 2.4 Theinhomogeneousacousticwaveequation–aerodynamicsound 165 2.4.1 Theinhomogeneouswaveequation 167 2.4.2 Lighthill’sacousticanalogy 174 2.4.3 Theeffectsofthepresenceofsolidbodiesintheflow 177 2.4.4 ThePowell–Howetheoryofvortexsound 180 2.5 Flowductacoustics 183 References 187 Nomenclature 188 3 Interactions between sound waves and solid structures 193 3.1 Introduction 193 3.2 Fundamentalsoffluid–structureinteractions 194 3.3 Soundradiationfromaninfiniteplate–wave/boundarymatching concepts 197 3.4 Introductoryradiationratioconcepts 203 3.5 Soundradiationfromfreebendingwavesinfiniteplate-typestructures 207 3.6 Soundradiationfromregionsinproximitytodiscontinuities–pointand lineforceexcitations 216 x Contents 3.7 Radiationratiosoffinitestructuralelements 221 3.8 Somespecificengineering-typeapplicationsofthereciprocityprinciple 227 3.9 Soundtransmissionthroughpanelsandpartitions 230 3.9.1 Soundtransmissionthroughsinglepanels 232 3.9.2 Soundtransmissionthroughdouble-leafpanels 241 3.10 Theeffectsoffluidloadingonvibratingstructures 244 3.11 Impactnoise 247 References 249 Nomenclature 250 4 Noise and vibration measurement and control procedures 254 4.1 Introduction 254 4.2 Noiseandvibrationmeasurementunits–levels,decibelsandspectra 256 4.2.1 Objectivenoisemeasurementscales 256 4.2.2 Subjectivenoisemeasurementscales 257 4.2.3 Vibrationmeasurementscales 259 4.2.4 Additionandsubtractionofdecibels 261 4.2.5 Frequencyanalysisbandwidths 263 4.3 Noiseandvibrationmeasurementinstrumentation 267 4.3.1 Noisemeasurementinstrumentation 267 4.3.2 Vibrationmeasurementinstrumentation 270 4.4 Relationshipsforthemeasurementoffree-fieldsoundpropagation 273 4.5 Thedirectionalcharacteristicsofsoundsources 278 4.6 Soundpowermodels–constantpowerandconstantvolumesources 279 4.7 Themeasurementofsoundpower 282 4.7.1 Free-fieldtechniques 282 4.7.2 Reverberant-fieldtechniques 283 4.7.3 Semi-reverberant-fieldtechniques 287 4.7.4 Soundintensitytechniques 290 4.8 Somegeneralcommentsonindustrialnoiseandvibrationcontrol 294 4.8.1 Basicsourcesofindustrialnoiseandvibration 294 4.8.2 Basicindustrialnoiseandvibrationcontrolmethods 295 4.8.3 Theeconomicfactor 299 4.9 Soundtransmissionfromoneroomtoanother 301 4.10 Acousticenclosures 304 4.11 Acousticbarriers 308 4.12 Sound-absorbingmaterials 313 4.13 Vibrationcontrolprocedures 320