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ARTICLEHISTORYRECEIVED18JUNE201430APRIL2015ACCEPTED1MAY2015HANDLINGEDITORHOUYANGAVAILABLEONLINE27MAY2015SINCETHEEARLY1920S,AUTOMOTIVEDISCBRAKESQUEALHASCAUSEDWARRANTYISSUESANDCUSTOMERDISSATISFACTIONDESPITEAGOODDEALOFPROGRESSACHIEVED,PREDICTINGBRAKESQUEALRIALSUPPLIERSINCLUDESTICKPARAMETRIC,3COUPLINGOFANALYSEDUSINGCONTENTSLISTSAVAILABLEATSCIENCEDIRECTJOURNALHOMEPAGEWWWELSEVIERCOM/LOCATE/JSVIJOURNALOFSOUNDANDVIBRATIONJOURNALOFSOUNDANDVIBRATION35220151291410022460X/DIMENSIONSINMMFIG2ACOUSTICBOUNDARYELEMENTWRAPPINGMESHOFTHEPADONPLATESYSTEMCUTOPENFORILLUSTRATIONTABLE1MATERIALPROPERTIESUSEDINSTRUCTURALCALCULATIONSINORDERTOEXTRACTSURFACEVELOCITIESANDNUMBEROFFINITEANDBOUNDARYELEMENTSGRAYEDOUTCOLUMNUSEDFORMODELSIIIIMODELGEOMETRYLININGDOFSFEMNODESDOFSBEMNODESSTRUCTURALMATERIALCONSTANTPLATEDISCLININGBACKPLATEIPLATEISOTROPIC631213,978EGPA210180849669520305030KGM377448025II30,44329,789EGPA11021036,29614,909028030ANNULARDISCKGM378007200IIIANISOTROPIC30,41535,562EIJGPA146TABLEA120736,75017,777029030KGM3710025007860TABLE2LININGMATERIALPROPERTIESADOPTEDFROM39OFTHEANISOTROPICPADONDISCMODELATDIFFERENTPRESSURESMATERIALPOINTCONSTANTMP0AT1KPAMP1AT05MPAMP2AT25MPAMP3AT50MPAMP4AT80MPAE33GPA1919254043E22E11GPA128128130131132G12GPA2020212223G13G23GPA40404244461221049049041032030231300800801050110115323100800801050110115SOBERST,JCSLAI/JOURNALOFSOUNDANDVIBRATION3522015129141132THECOULOMBFRICTIONMODELWITHACONSTANTFRICTIONCOEFFICIENTANDTHEFINITESLIDING,SURFACETOSURFACECONTACTDEFINITIONINABAQUS68436ISAPPLIEDTHEFINITESLIDINGDEFINITIONALLOWSARBITRARYTRANSLATION,ROTATIONANDINCOMBINATIONWITHAHARDOVERCLOSUREOPTIONASCONTACTNORMALBEHAVIOUR,ALSOSEPARATIONOFTHECONTACTNODES36SURFACENORMALVELOCITIESASANINPUTTOTHEACOUSTICFASTMULTIPOLEBOUNDARYELEMENTMETHODVAONE2010,ESI41WEREEXTRACTEDFROMRESULTSOFTHEDSAOFTHESTRUCTURALFINITEELEMENTMODELTOCALCULATETHEUNKNOWNACOUSTICPRESSUREONTHESURFACEOFTHEWRAPPINGMESH42THEDSAINVOLVESESTABLISHMENTOFABASESTATEWITHNONLINEARSTATICSTEPS,ANDAPPLICATIONOFCONTACTPRESSURE,ROTATION,ANDASYMMETRICFRICTIONSTIFFNESSMOREDETAILSOFTHECOMPUTATIONALPROCEDUREOFTHESTRUCTURALANALYSISAREGIVENIN33STRUCTURALHEXAHEDRALINCOMPATIBLEMODEELEMENTSANDACOUSTICLINEARTET3ELEMENTSWEREUSEDFORTHEFINITEELEMENTMESHANDTHEBOUNDARYELEMENTWRAPPINGMESHFIG2RESPECTIVELYTHEMATERIALPROPERTIESANDTHENUMBEROFELEMENTSUSEDAREGIVENINTABLES1AND2THEANISOTROPICPADONDISCMODELISDIFFERENTFROMTHEISOTROPICMODELINTHATITAPPROXIMATESPRESSUREDEPENDENTLININGMATERIALPROPERTIESCF39AWATERTIGHTWRAPPINGMESH36USEDINTHEACOUSTICBOUNDARYELEMENTMETHOD,ACCORDINGTOTHEGAUSSTHEOREM,ALLOWSTHECALCULATIONOFSURFACEPRESSURESONTHESURFACEOFASINGLEVOLUMETHEREALPARTOFACOMPLEXEIGENVALUEOBTAINEDFROMTHESTRUCTURALFINITEELEMENTMODELINDICATESTHESTABILITYOFLINEARVIBRATIONS36THEVIBRATIONMODESOFTHEMODELARECLASSIFIEDACCORDINGTOTHEVIBRATIONMODESOFADISCWITHOUTTHEHATSECTIONASMNLQHERE,M,NSTANDRESPECTIVELYFORTHENUMBEROFOUTOFPLANENODALCIRCLESANDDIAMETERSANDL,QRESPECTIVELYFORTHENUMBEROFINPLANENODALCIRCLESANDNODALRADIALLINESOFTHEDISC36THESPEEDOFSOUNDWASSETTOC340M/SANDTHEFLUIDSDENSITYTO13KGM3ALLSIMULATIONSWERECONDUCTEDACCORDINGTOTHEGUIDELINESESTABLISHEDIN36THEACOUSTICPOWERWASCALCULATEDFROMTHEREALPARTOFTHEINTEGRALOFTHESOUNDINTENSITYOVERASURFACEENCLOSINGTHEMODELWITH12REZPVNSDC26C271WHEREP,VNSANDREPRESENTTHESOUNDPRESSURE,THECOMPLEXCONJUGATEOFTHESURFACEVELOCITYANDTHESURFACEAREA,RESPECTIVELY42THERADIATIONEFFICIENCY,ISTHERATIOOFAVERAGEACOUSTICPOWERRADIATEDPERUNITAREAOFAVIBRATINGSURFACETOTHEAVERAGEACOUSTICPOWERRADIATEDPERUNITAREAOFAPISTONTHATISVIBRATINGWITHTHESAMEAVERAGEMEANSQUAREVELOCITYATAFREQUENCYFORWHICHTHEPISTONSCIRCUMFERENCEISMUCHLARGERTHANITSACOUSTICWAVELENGTH43CV22WITHCORRESPONDINGTOTHERADIATEDACOUSTICPOWER,THESURFACEAREAOFTHEVIBRATINGSTRUCTUREANDV2THESPATIALAVERAGEOFTHEMEANSQUAREVELOCITYRESPONSEOFTHESTRUCTURE3ACOUSTICRADIATIONOFSIMPLEMODELSOFBRAKESYSTEMS31PADONPLATEMODELACOUSTICPOWERFIG3DEPICTSTHERADIATEDACOUSTICPOWERLEVELSWITHRESONANCESF1F4INTHEFREQUENCYRANGEOF2564KHZFORTHEPADONPLATEMODELSUBJECTEDTOHARMONICCONTACTPRESSUREEXCITATIONS1KPATO8MPAANDDIFFERENTFRICTIONCOEFFICIENTS005065EDMARKSTHEFREQUENCYINTERVALSWHEREENERGYISGENERATEDRATHERTHANDISSIPATED1,11,44ASOUNDPRESSURELEVELOFATLEAST70DBATADISTANCEOF05MFROMTHEBRAKEROTORISCONSIDEREDASSQUEALACCORDINGTOSAEJ252132FORAMONOPOLERADIATOR,THISISEQUIVALENTTOANACOUSTICPOWERLEVELOF75DBWHICHISDRAWNASAHORIZONTALDOTDASHEDLINEINFIG3HERE,RESONANCEF1ISDOMINATEDBYTHEPLATEMOTION,WITHRESONANCEF2TOF4DOMINATEDBYTHEPADMOTIONTHEACOUSTICPOWERLEVELSATF2TOF4VARYGREATLYWITHFORALLPRESSURESTHERESULTSHERESHOWTHATINPLANEPADMODESESPECIALLYPXINTHESLIDINGXDIRECTIONATF3NOTONLYCAUSEMOSTOFTHEFEEDINENERGYBUTTHATTHEYAREALSOACOUSTICALLYRELEVANTHEREESPECIALLYRESONANCEF3PADMODEDOMINATEDMOTIONINTHESLIDINGDIRECTIONISWITHINTHERANGEOFSQUEALFREQUENCIESEXPERIMENTALLYDETECTEDBYCHEN4EVENTHOUGHONLYACONSTANTFRICTIONLAWHASBEENAPPLIEDRADIATIONEFFICIENCYFIG4DEPICTSTHERADIATIONEFFICIENCYFORTHEPADONPLATEMODELFORDIFFERENTCONTACTPRESSUREEXCITATIONS1KPATO8MPAANDFRICTIONCOEFFICIENTS005065RESONANCEFREQUENCIESF1TOF4AREINDICATEDBYVERTICALLINE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