简单的数字制动模型中的尖叫噪声【中文9500字】
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上传时间：2018-03-21
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- 关 键 词：
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简单
数字
制动
模型
中的
尖叫
噪声
中文
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简单的数字制动模型中的尖叫噪声【中文9500字】,简单,数字,制动,模型,中的,尖叫,噪声,中文
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JOURNALOFSOUNDANDVIBRATION3522015129141SQUEALNOISEINSIMPLENUMERICALBRAKEMODELSSOBERSTN,JCSLAIACOUSTICSDIMENSIONSINMMFIG2ACOUSTICBOUNDARYELEMENTWRAPPINGMESHOFTHEPADONPLATESYSTEMCUTOPENFORILLUSTRATIONTABLE1MATERIALPROPERTIESUSEDINSTRUCTURALCALCULATIONSINORDERTOEXTRACTSURFACEVELOCITIESANDNUMBEROFFINITEANDBOUNDARYELEMENTSGRAYEDOUTCOLUMNUSEDFORMODELSIIIIMODELGEOMETRYLININGDOFSFEMNODESDOFSBEMNODESSTRUCTURALMATERIALCONSTANTPLATEDISCLININGBACKPLATEIPLATEISOTROPIC631213,978EGPA210180849669520305030KGM377448025II30,44329,789EGPA11021036,29614,909028030ANNULARDISCKGM378007200IIIANISOTROPIC30,41535,562EIJGPA146TABLEA120736,75017,777029030KGM3710025007860TABLE2LININGMATERIALPROPERTIESADOPTEDFROM39OFTHEANISOTROPICPADONDISCMODELATDIFFERENTPRESSURESMATERIALPOINTCONSTANTMP0AT1KPAMP1AT05MPAMP2AT25MPAMP3AT50MPAMP4AT80MPAE33GPA1919254043E22E11GPA128128130131132G12GPA2020212223G13G23GPA40404244461221049049041032030231300800801050110115323100800801050110115DSAINDICATESNEGATIVETOTALDISSIPATIVEENERGY33FORTHESEPADMODES,HENCEAPOTENTIALFORSQUEALGENERATIONTHEUNSTABLEFREQUENCIESOFTHEINPLANEPADMODESHAVEBEENFOUNDTOCORRESPONDTOTHESQUEALFREQUENCIESOBSERVEDBYCHEN,THUSVALIDATINGTHENUMERICALMETHODOLOGYFORVIBRATIONANALYSISINTERESTINGLY,THESAMEBEHAVIOUROFINPLANEPADMODESOFTHEPADONPLATEMODELPREDICTEDTOBESTABLEBYTHECEA,LARGECHANGESOFFREQUENCIESWITHCONTACTPRESSUREANDFRICTIONCOEFFICIENTANDENERGYPROVISIONINSTEADOFDISSIPATIONHASBEENFOUNDFORTHEPADONDISCMODELSHENCE,THEVALIDATEDRESULTSOFTHEVIBRATIONANALYSISFORTHEPADONPLATEMODELAREUSEDTOASSESSTHEAUDIBLESQUEALPROPENSITYUSINGTHEACOUSTICBOUNDARYELEMENTMETHODTHISMETHODOLOGYISTHENAPPLIEDTOSTUDYTHEPADONDISCMODELWHICHISASIMPLIFIEDBUTMOREREALISTICMODELOFABRAKESYSTEMSS132SOBERST,JCSLAI/JOURNALOFSOUNDANDVIBRATION3522015129141THECOULOMBFRICTIONMODELWITHACONSTANTFRICTIONCOEFFICIENTANDTHEFINITESLIDING,SURFACETOSURFACECONTACTDEFINITIONINABAQUS68436ISAPPLIEDTHEFINITESLIDINGDEFINITIONALLOWSARBITRARYTRANSLATION,ROTATIONANDINCOMBINATIONWITHAHARDOVERCLOSUREOPTIONASCONTACTNORMALBEHAVIOUR,ALSOSEPARATIONOFTHECONTACTNODES36SURFACENORMALVELOCITIESASANINPUTTOTHEACOUSTICFASTMULTIPOLEBOUNDARYELEMENTMETHODVAONE2010,ESI41WEREEXTRACTEDFROMRESULTSOFTHEDSAOFTHESTRUCTURALFINITEELEMENTMODELTOCALCULATETHEUNKNOWNACOUSTICPRESSUREONTHESURFACEOFTHEWRAPPINGMESH42THEDSAINVOLVESESTABLISHMENTOFABASESTATEWITHNONLINEARSTATICSTEPS,ANDAPPLICATIONOFCONTACTPRESSURE,ROTATION,ANDASYMMETRICFRICTIONSTIFFNESSMOREDETAILSOFTHECOMPUTATIONALPROCEDUREOFTHESTRUCTURALANALYSISAREGIVENIN33STRUCTURALHEXAHEDRALINCOMPATIBLEMODEELEMENTSANDACOUSTICLINEARTET3ELEMENTSWEREUSEDFORTHEFINITEELEMENTMESHANDTHEBOUNDARYELEMENTWRAPPINGMESHFIG2RESPECTIVELYTHEMATERIALPROPERTIESANDTHENUMBEROFELEMENTSUSEDAREGIVENINTABLES1AND2THEANISOTROPICPADONDISCMODELISDIFFERENTFROMTHEISOTROPICMODELINTHATITAPPROXIMATESPRESSUREDEPENDENTLININGMATERIALPROPERTIESCF39AWATERTIGHTWRAPPINGMESH36USEDINTHEACOUSTICBOUNDARYELEMENTMETHOD,ACCORDINGTOTHEGAUSSTHEOREM,ALLOWSTHECALCULATIONOFSURFACEPRESSURESONTHESURFACEOFASINGLEVOLUMETHEREALPARTOFACOMPLEXEIGENVALUEOBTAINEDFROMTHESTRUCTURALFINITEELEMENTMODELINDICATESTHESTABILITYOFLINEARVIBRATIONS36THEVIBRATIONMODESOFTHEMODELARECLASSIFIEDACCORDINGTOTHEVIBRATIONMODESOFADISCWITHOUTTHEHATSECTIONASMNLQHERE,M,NSTANDRESPECTIVELYFORTHENUMBEROFOUTOFPLANENODALCIRCLESANDDIAMETERSANDL,QRESPECTIVELYFORTHENUMBEROFINPLANENODALCIRCLESANDNODALRADIALLINESOFTHEDISC36THESPEEDOFSOUNDWASSETTOC340M/SANDTHEFLUIDSDENSITYTO13KGM3ALLSIMULATIONSWERECONDUCTEDACCORDINGTOTHEGUIDELINESESTABLISHEDIN36THEACOUSTICPOWERWASCALCULATEDFROMTHEREALPARTOFTHEINTEGRALOFTHESOUNDINTENSITYOVERASURFACEENCLOSINGTHEMODELWITH1RERZ2PVND1WHEREP,VNANDREPRESENTTHESOUNDPRESSURE,THECOMPLEXCONJUGATEOFTHESURFACEVELOCITYANDTHESURFACEAREA,RESPECTIVELY42THERADIATIONEFFICIENCY,ISTHERATIOOFAVERAGEACOUSTICPOWERRADIATEDPERUNITAREAOFAVIBRATINGSURFACETOTHEAVERAGEACOUSTICPOWERRADIATEDPERUNITAREAOFAPISTONTHATISVIBRATINGWITHTHESAMEAVERAGEMEANSQUAREVELOCITYATAFREQUENCYFORWHICHTHEPISTONSCIRCUMFERENCEISMUCHLARGERTHANITSACOUSTICWAVELENGTH432CV2WITHCORRESPONDINGTOTHERADIATEDACOUSTICPOWER,THESURFACEAREAOFTHEVIBRATINGSTRUCTUREANDV2THESPATIALAVERAGEOFTHEMEANSQUAREVELOCITYRESPONSEOFTHESTRUCTURE3ACOUSTICRADIATIONOFSIMPLEMODELSOFBRAKESYSTEMS31PADONPLATEMODELACOUSTICPOWERFIG3DEPICTSTHERADIATEDACOUSTICPOWERLEVELSWITHRESONANCESF1F4INTHEFREQUENCYRANGEOF2564KHZFORTHEPADONPLATEMODELSUBJECTEDTOHARMONICCONTACTPRESSUREEXCITATIONS1KPATO8MPAANDDIFFERENTFRICTIONCOEFFICIENTS005065EDMARKSTHEFREQUENCYINTERVALSWHEREENERGYISGENERATEDRATHERTHANDISSIPATED1,11,44ASOUNDPRESSURELEVELOFATLEAST70DBATADISTANCEOF05MFROMTHEBRAKEROTORISCONSIDEREDASSQUEALACCORDINGTOSAEJ252132FORAMONOPOLERADIATOR,THISISEQUIVALENTTOANACOUSTICPOWERLEVELOF75DBWHICHISDRAWNASAHORIZONTALDOTDASHEDLINEINFIG3HERE,RESONANCEF1ISDOMINATEDBYTHEPLATEMOTION,WITHRESONANCEF2TOF4DOMINATEDBYTHEPADMOTIONTHEACOUSTICPOWERLEVELSATF2TOF4VARYGREATLYWITHFORALLPRESSURESTHERESULTSHERESHOWTHATINPLANEPADMODESESPECIALLYPXINTHESLIDINGXDIRECTIONATF3NOTONLYCAUSEMOSTOFTHEFEEDINENERGYBUTTHATTHEYAREALSOACOUSTICALLYRELEVANTHEREESPECIALLYRESONANCEF3PADMODEDOMINATEDMOTIONINTHESLIDINGDIRECTIONISWITHINTHERANGEOFSQUEALFREQUENCIESEXPERIMENTALLYDETECTEDBYCHEN4EVENTHOUGHONLYACONSTANTFRICTIONLAWHASBEENAPPLIEDRADIATIONEFFICIENCYFIG4DEPICTSTHERADIATIONEFFICIENCYFORTHEPADONPLATEMODELFORDIFFERENTCONTACTPRESSUREEXCITATIONS1KPATO8MPAANDFRICTIONCOEFFICIENTS005065RESONANCEFREQUENCIESF1TOF4AREINDICATEDBYVERTICALLINESANDTHEINTERVALSWHEREENERGYISPROVIDEDEDO0CF1,44AREHIGHLIGHTEDBYHORIZONTALARROWSITAPPEARSTHATFORAGIVEN,THERADIATIONEFFICIENCYISALMOSTPRESSUREINDEPENDENTHIGHEREXCITATIONAMPLITUDESLEADTOPROPORTIONALLYHIGHERSOUNDRADIATIONFORFREQUENCIESAROUND545596KHZFIG4ITWOULDBEQUITEEFFICIENTFORSQUEALTODEVELOP41ONTHEOTHERHAND,ATAROUND4553KHZBETWEENF2ANDF3,STRONGERVIBRATIONSWOULDBEREQUIREDFORSQUEALGENERATIONFURTHER,CHEN4REPORTEDINSTANTANEOUSMODESQUEALATAROUNDAFREQUENCYOF57KHZWHERETHERADIATIONEFFICIENCYISFOUNDTOBEMAXIMUMHEREFORATHICKANNULARDISCSUBJECTEDTOMULTIMODALEXCITATIONBUTWITHOUTFRICTIONALCONTACT,LEEANDSINGH45FOUNDSTRONGCHANGESINTHEACOUSTICPOWERLEVELSANDRADIATIONEFFICIENCIESOWINGTOSELFANDMUTUALRADIATIONEFFECTSBETWEENEITHEROUTOFPLANEMODESWITHNMORBETWEENOUTOFPLANEANDRADIALINPLANEMODESIFNQHERE,BYINCORPORATINGFRICTIONWITHHARMONICCONTACTPRESSUREEXCITATIONACTINGOVERTHEWHOLEPAD36,STRONGCHANGESINTHERADIATIONEFFICIENCYAREOBSERVEDMOSTLYINTHESIDEBANDSOFPADMODERESONANCESFIG4SOBERST,JCSLAI/JOURNALOFSOUNDANDVIBRATION3522015129141133FIG3ACOUSTICPOWERLEVELSFORTHEPADONPLATESYSTEMOVERFREQUENCYFORPRESSURESOF1KPA,05,25,5AND8MPAANDFRICTIONCOEFFICIENTS,005,025,045AND065ASREFERENCESQUEALOFAMONOPOLEWITH70DBRECORDEDIN05MDISTANCEISPLOTTEDASWELLFIG4RADIATIONEFFICIENCIES,FORPRESSURES1KPA,05MPA,25MPA,5MPAAND8MPAOVERFRICTIONCOEFFICIENTS,AF005025,045,065GRANGEOFSQUEALFREQUENCIESANDTHEPLATESFIRSTOUTOFPLANERESONANCEFREEFREEBOUNDARYCONDITIONSOBSERVEDINEXPERIMENTSBYCHEN4OFASIMILARPADONPLATESYSTEMAREALSODEPICTEDEDINDICATESINTERVALSOFNEGATIVEDISSIPATEDENERGYSTUDIEDINOBERSTANDLAI44RADIATIONEFFICIENCYANDPHASERELATIONSHIPWHILETHERESEEMSTOBESOMECORRELATIONSBETWEENTHEFREQUENCYINTERVALSOFNEGATIVEDISSIPATEDENERGYANDTHECHANGESINRADIATIONEFFICIENCYFIG4,THEINFLUENCEOFTHEPHASEDIFFERENCEOFTHEVELOCITYRESPONSEBETWEENTHEPADSCENTREANDTHEPLATESCENTREONISEXAMINEDFIG5SHOWSTHATTHERADIATIONEFFICIENCYCHANGESTHEMOSTINTHEFREQUENCYRANGE4761KHZONLY005AND065WITHINTHISFREQUENCYRANGEBOXEDINFIG5,THEVIBRATIONVELOCITYINTHEYDIRECTIONOFTHEPADANDTHATOFTHEPLATEFOR005ARELARGELYINPHASEFORFREQUENCIES4854KHZ,OTHERWISEOUTOFPHASEFOR065,THEPADSVIBRATIONVELOCITYSPHASEISMOSTLYOUTOFPHASEWITHTHEPLATESPHASEINTHESLIDINGXDIRECTION,THEPHASEDIFFERENCEBETWEENTHEPADSVIBRATIONVELOCITYANDTHATOFTHEPLATEDOESNOTCHANGEMUCHASTHEFRICTIONCOEFFICIENTISINCREASEDFROM005TO065INTHEOUTOFPLANEDIRECTIONZ,THEPADSVIBRATIONVELOCITYANDTHEPLATESAREMOSTLYINPHASEFOR005BUTAREMOSTLYOUTOFPHASEWHENISINCREASEDTO065THISPHASEDIFFERENCEINTHEZDIRECTIONCORRELATESWELLWITHTHECHANGEINTHERADIATIONEFFICIENCYWITHFIG4,SIMILARTOTHEMECHANISMDESCRIBEDBYMATSUIETAL46APHASEDIFFERENCEBETWEENNORMALANDFRICTIONFORCESCAUSESSQUEALOWINGTOENERGYBEINGPROVIDEDCFVONWAGNER16ASTHENUMERATORINEQ2GROWSTHEONLYEXPLANATIONFORA134SOBERST,JCSLAI/JOURNALOFSOUNDANDVIBRATION3522015129141FIG5PHASEDIFFERENCEVELOCITYBETWEENPLATEANDPAD,CALCULATEDFORY,XANDZDIRECTIONINPOINTPOFTHEPLATEANDTHEPADSCENTREPOINTINTHEZDIRECTIONTHERADIATIONEFFICIENCYISDEPICTEDBOXEDAREASHOWSFREQUENCYINTERVALWHERECHANGESMOSTPRESSURE05MPAFRICTIONCOEFFICIENTS005AND065DECREASINGISASTRONGERINCREASEOFTHEVIBRATIONVELOCITIES,ACCOMPANIEDBYGROWINGPHASEDIFFERENCEBETWEENTHEPLATEANDTHEPADINTHEOUTOFPLANEDIRECTION32ISOTROPICPADONDISCMODELACOUSTICPOWERFIG6DEPICTSOFTHEISOTROPICPADONDISCMODELSUBJECTEDTOHARMONICCONTACTPRESSUREEXCITATIONFORDIFFERENTPRESSURESOF0001,025,05,25,5AND8MPATHREEPADMODESAREFOUNDBELOW7KHZINPLANERADIALPRANDTANGENTIALPTMODESANDTHEROTATIONOFTHEPADAROUNDITSZAXISPROTITCANBESEENTHAT1SQUEALCOULDALREADYBEDETECTEDATPRESSURESASLOWAS1KPAWITHEXCEEDING75DBATSOMEFREQUENCIESAND2INPLANEPADMODESCOMPAREDTOTHEINPLANEMODESOFTHEDISCF4ANDCFKINETICENERGYSPECTRUM1AREALLACOUSTICALLYRELEVANTFORPRESSURESLESSTHANOREQUALTO05MPAFORHIGHERPRESSURES,ONLYPTREMAINSACOUSTICALLYRELEVANTBYINCREASINGTHEFRICTIONCOEFFICIENT,THEACOUSTICPOWERLEVELINCREASESINTHESIDEBANDSOFRESONANCESF7PR,F8PTANDF11PROTMODESPRANDPROTSEEMTOBEIMPORTANTINDEVELOPINGBRAKENOISEATINITIATINGTHEBRAKINGPROCESSWHENBOTHTHECONTACTPRESSUREANDTHEFRICTIONCOEFFICIENTARESTILLLOWASINDICATEDBYMORERESONANCESINTHEACOUSTICPOWERSPECTRUMATPRESSURESLESSTHAN05MPAPADMODEINSTABILITIESINASIMILARBRAKESYSTEMHAVEBEENSHOWNTOCAUSECHAOTICINTERMITTENTVIBRATION,TRIGGERINGUNSTABLEQUASIPERIODICMOTIONOFTHEDISCAT1KPA11SIMILARTOTHEISOTROPICPADONDISCMODELFIG6,FIG7SHOWSTHATTHEACOUSTICPOWERLEVELTHOSEOFTHEANISOTROPICPADONDISCMODELGROWSWITHINCREASINGPRESSURESORFRICTIONCOEFFICIENTSESPECIALLYATRESONANCESOFPADMODESPTANDPROTPRANDPROTVANISHAFTERTHEPRESSUREISINCREASEDTOOVER05MPAALTHOUGHTHESEAREINPLANEPADMODES,THEYAREACOUSTICALLYRELEVANTASINDICATEDBYTHEIRPEAKSINTHEACOUSTICPOWERSPECTRATHEDEPENDENCYOFTHERADIALANDROTATIONALPADMODESONLOWPRESSURESSUPPORTSTHEASSUMPTIONOFBRAKENOISEDEVELOPINGATTHEINITIALPHASEOFABRAKEAPPLICATIONWHENTHEPRESSUREISBEINGBUILTUPANDTHEFRICTIONCOEFFICIENTISRATHERLOWNEXT,THEACOUSTICPOWERLEVELSATALLRESONANCEFREQUENCIESRATHERTHANOVERTHEWHOLEFREQUENCYRANGEARECALCULATEDFIG8DEPICTSTHEACOUSTICPOWERLEVELSOFTHEMOSTPROMINENTOFTHE21MODESINTHEFREQUENCYRANGEUPTO7KHZTHICK,SOLIDLINESOFTHEISOTROPICPADONDISCMODELAT1KPAWITHCOMPLIANTPADCONSTRAINTSCOMPAREDTOACOUSTICPOWERLEVELSOFSTIFFENEDPADCONSTRAINTS1THECRITICALFRICTIONCOEFFICIENTSDETERMINEDBYTHECEAATWHICHTHEOUTOFPLANEDISCMODESMERGEAREDENOTEDBYTP1ANDTP2THEPADMODES,PR,PTANDPROT,OCCURATAROUND359,366AND542KHZ,RESPECTIVELYANDTHEN3ANDN5DISCMODEPAIRCOUPLESTOBECOMEUNSTABLETHEN5,IETHEUNSTABLE0500DISCMODERADIATESLESSACOUSTICPOWERTHANTHEUNSTABLEN3DISCMODEWITHTHEMAXIMUMACOUSTICPOWEROCCURRINGPASTTP2ATABOUT055WITHINCREASINGTHEACOUSTICSOBERST,JCSLAI/JOURNALOFSOUNDANDVIBRATION3522015129141135FIG6ACOUSTICPOWERLEVELS,OFISOTROPICPADONDISCSYSTEMRESONANCESMARKEDFROMF1TOF15PADMODESPR,PTANDPROTF503700ANDF1305700MODESPREDICTEDTOBEUNSTABLEBYCEA,ADDITIONALLYMARKEDBYVERTICALDASHEDLINESASREFERENCESQUEALOFAMONOPOLEWITH70DBSPLRECORDEDIN05MDISTANCEISPLOTTEDASWELLFIG7ACOUSTICPOWERLEVELSOFANISOTROPICPADONDISCMODELWITHPRESSURESOF1KPA,05,25,5AND8MPAANDFRICTIONCOEFFICIENTS005,025,045AND065,RESPECTIVELYMAXIMALACOUSTICPEAKPOWERLEVELSAT1KPAANDAT8MPAOFTHEISOTROPICPADONDISCSYSTEMAREINDICATEDBYHORIZONTALARROWSPOWERLEVELSOFTHEPADMODESEXHIBITSTRONGOSCILLATORYBEHAVIOURDISCMODES,SUCHAS00270AND00370,ALSOOSCILLATESIMILARTOTHEPADMODESWITHSTIFFERPADCONSTRAINTSIE10PERCENTOFEACHOFTHE4EDGESONTHETOPSURFACEOFTHEPADCONSTRAINEDTHEPADMODESDISAPPEARFROMTHEACOUSTICPOWERSPECTRAASSHOWNIN1ANDNOFLUCTUATIONINDISCMODESAREOBSERVEDHENCETHISSUGGESTSTHATPADMODESARETHEREASONFORTHEOSCILLATORYALMOSTFLUCTUATINGBEHAVIOURINTHEACOUSTICPOWERSPECTRAINFIG8RADIATIONEFFICIENCYFIG9DEPICTSTHERADIATIONEFFICIENCYSPECTRAOFTHEISOTROPICPADONDISCMODELWITH20COMBINATIONSOFCONTACTPRESSURES1KPA,05,25,5AND8MPAANDFRICTIONCOEFFICIENTS005,025,045,065TWOFREQUENCYINTERVALSF2236KHZAND4554KHZRELATEDTOPADMODESPRSIMILARTOTHEPADONPLATESYSTEMVERYLITTLEINFLUENCEONTHERADIATIONEFFICIENCYFORTHEDISCSINPLANESHEARMODE,L0F4,IS097AT005BUTDROPSTOVALUESLOWERTHAN063FORZ025MINIMUMVALUENOTDEPICTEDINFIG9THE136SOBERST,JCSLAI/JOURNALOFSOUNDANDVIBRATION3522015129141FIG8VARIATIONOFACOUSTICPOWERLEVELWITHTHEFRICTIONCOEFFICIENT1KPAPADMODESCAUSETHEACOUSTICPOWERTOOSCILLATEWITHFRICTIONCOEFFICIENTDOTTEDLINESARESTABLEMODESORMODESWHICHDONOTSHOWSIGNIFICANTLYDIFFERENTBEHAVIOURTOMODESPLOTTEDWITHSOLIDLINESFIG9RADIATIONEFFICIENCIES,OFISOTROPICPADONDISCWITHCHANGINGPRESSURE,PAF103052558GMPA,ANDVARIATIONSINFRICTIONCOEFFICIENT,AF005025045065GTWOFREQUENCYINTERVALSOFCHANGESINFREQUENCIESFOFPADMODESPRPTANDPROTEXTRACTEDFROMCEARADIATIONEFFICIENCYATTHESIDEBANDSOFRESONANCESF7,F8ANDF11CORRESPONDINGTOTHEPADMODESPRASCHANGESINPADMODESEIGENFREQUENCIESFAREMORESEVEREFORTHEANISOTROPICPADONDISCSYSTEMANDTHELININGMATERIALPROPERTIESCHANGE,THEZONESOFPADMODESINFLUENCEOVERLAPFRICTIONCOEFFICIENTANDPRESSUREBETWEEN18AND3KHZ,ALTHOUGHINCREASESWITHPRESSURE,ITSINCREASEWITHTHEFRICTIONCOEFFICIENTISMUCHGREATER,ESPECIALLYAT23KHZINGENERALTHERADIATIONEFFICIENCYOFTHEANISOTROPICPADONDISCMODELISMUCHLOWERTHANFORTHEISOTROPICPADONDISCMODEL,WHICHSOMETIMESEXCEEDSEVENONEWHILEFORTHEANISOTROPICPADONDISCMODELTHEACOUSTICPOWERLEVELSARESIMILARTOTHOSEOFTHEISOTROPICPADONDISCMODEL,THERADIATIONEFFICIENCYCHANGESWITHPRESSUREANDFRICTIONCOEFFICIENTAREGREATEROWINGTOCHANGESINLININGMATERIALPROPERTIESHOWEVER,THERADIATIONEFFICIENCIESFORBOTHTHEISOTROPICANDTHEANISOTROPICPADONDISCMODELWITHFRICTIONAREMUCHHIGHERTHANTHOSEOFANNULARDISCSONLYWITHMODALRADIATIONEFFICIENCIESMN1FORTHEOUTOFPLANEMODESINTHICKDISCSBEING01005,02044AND030562COMPAREDWITH012NOTVISIBLEATF1,068AND095OFTHEPADONDISCMODEL,RESPECTIVELY4INSTANTANEOUSMODESINTHEEXPERIMENTALSTUDYOFASLIDERONPLATESYSTEM,SQUEALHASBEENSHOWNTODEVELOPATFREQUENCIESLOWERTHANTHEFLEXIBLEMODERESONANCEFREQUENCIESOFTHEPLATE4THISINSTANTANEOUSMODESQUEAL4COULDBEINDUCEDBYPADMODEINSTABILITIESANDHENCETHEIRACOUSTICDIRECTIVITYPATTERNSARESTUDIEDNEXTTABLE3FORTHEPURPOSEOFCALCULATINGTHEDIRECTIVITYPATTERN,AFIELDPOINTMESHWITHELEMENTSOF1CMLENGTHANDACUBICSHAPE050505M3ISUSEDFOURSIDESOFTHECUTOPENCUBEARELABELLEDATODTHECONTACTPRESSUREWASSETTO1KPAWITHAFRICTIONCOEFFICIENTOF045THESURFACEVELOCITYDISTRIBUTIONNORMALVELOCITYDATASHOWSTHATAT5694HZ,ALTHOUGHTHEMODEPXOFTHEPADDOMINATESTHESYSTEMMOTION,THEPLATESMOTIONISALSOEXCITEDTHESOUNDPRESSUREFIELDPOINTMESHINDICATESTHATTHEDOMINANTACOUSTICRADIATIONISINTHEOUTOFPLANEDIRECTIONOFTHEPLATE,ASSHOWNFORSURFACESAANDDEVENTHOUGHTHEPADMOVESINPLANEASEXPECTED,THEFLUIDVELOCITYMAGNITUDECONTOURSSHOWTHATTHEVELOCITYMAGNITUDEINTHEDIRECTIONNORMALTOTHEPLATEISHIGHERTHANTHATINTHEPLANEOFTHEPLATEITCANBESEENFROMTHESOUNDPRESSURECONTOURSATAGIVENPHASETHATTHEPADBEHAVESLIKEAPULSATINGMONOPOLESURFACEDSHOWSAMUCHHIGHERVIBRATIONVELOCITYMAGNITUDETHANSURFACEA,SUGGESTINGSIGNIFICANTCONTRIBUTIONTOTHEACOUSTICRADIATIONFROMTHEPADORTHEFRICTIONCONTACTSURFACEORBOTH,INADDITIONTOTHEPLATESRADIATIONTHEACOUSTICINTENSITYCONTOURSINDICATETHATTHEACOUSTICRADIATIONINTHEOUTOFPLANEDIRECTIONISDOMINANT,ESPECIALLYATTHESIDEOFTHEPADASWELLASINTHERADIALINPLANEDIRECTIONTHESURFACEVIBRATIONVELOCITYDISTRIBUTIONANDTHEACOUSTICRADIATIONOFTHEPADMODESPR,PTANDPROTOFTHEISOTROPICPADONDISCMODELAREGIVENINTABLE4,FOR1KPAAND045THEFIELDPOINTMESHCONSISTSOFELEMENTSOFLENGTHS155CMAND1CMAT3658AND5403HZ,RESPECTIVELY,CORRESPONDINGTOATLEAST6ELEMENTSPERWAVELENGTH42FORPR,THESURFACEVELOCITYDISTRIBUTIONREVEALSTHEN4DISCMODEATAROUND41KHZ,APPROXIMATELY550HZAWAYFROMTHEPADMODE355KHZ4VIEWS1AND2GIVETHEACOUSTICDIRECTIVITYPATTERNOFINSTANTANEOUSPRESSUREATONEPHASEONTHECUBICFIELDPOINTMESHFORTHEPADMODEPR,THERADIATIONPATTERNONSIDEAISTHATOFTHEN4DISCMODEWITHSTRONGSOUNDRADIATIONINTHERADIALDIRECTIONOFTHEPADTHEPADMODEPRANDTHESTILLACTIVEVIBRATINGN4DISCMODEACTTOGETHERTORADIATEHIGHSOUNDPRESSURELEVELWITHTHEFRINGEPATTERNOFTHEN4DISCMODEONSIDED,THESOUNDPRESSUREPATTERNDUETOTHEPADMOVINGINTHEINPLANERADIALDIRECTIONISTHATOFADIPOLEWITHITSLONGITUDINALAXISPERPENDICULARTOTHERESULTANTMOTIONOF1WITHMNODALCIRCLESANDNNODALDIAMETERS2MNQL,ACCORDINGTO27,38TABLE3DIRECTIVITYPATTERNOFPADMODEPXOFTHEISOTROPICPADONPLATEMODELSHOWINGTHEFORCEDRESPONSEDATA,SOUNDPRESSUREFIELDPOINTMESHWITHAPEAKSOUNDPRESSURELEVELSPLPOF61DB,THENORMALSURFACEVELOCITYINTHEFLUID,ANDTHESOUNDINTENSITYP1KPA,045138SOBERST,JCSLAI/JOURNALOFSOUNDANDVIBRATION3522015129141SOBERST,JCSLAI/JOURNALOFSOUNDANDVIBRATION3522015129141139TABLE4DIRECTIVITYPATTERNFORISOTROPICPADONDISCMODELSHOWINGFORCEDRESPONSEDATAANDFIELDPOINTMESHOFSOUNDPRESSURELEVELFORTHERADIAL,TANGENTIALANDROTATIONALPADMODESPR,PTANDPROT,RESPECTIVELYP1KPA,045THEPADTHEDIFFRACTIONNEARFIELDEFFECTSOFTHESOUNDWAVEARECLEARLYVISIBLE,ASINDICATEDBYTHERIPPLINGSOUNDPRESSUREWAVESTHETOPSIDEOFDVIEW2SHOWSADIPOLEWITHANAXISPERPENDICULARTOTHEMOTIONOFTHEPADTHETWOARROWSHIGHLIGHTHOWTHESOUNDPRESSUREPATTERNMOVESOVERONECYCLEINTHESAMEDIRECTIONASTHESPINNINGDISCTHEACOUSTICRADIATIONOFTHEPADISMOREIMPORTANTTHANONEMIGHTEXPECT,ESPECIALLYATTHEPADMODESRESONANCEFREQUENCIESBASEDONTHEIRRESULTSFROMACOUSTICHOLOGRAPHY,HENDRICXETAL47FOUNDTHATLOCALEFFECTSANDTHECONTACTATTHEPADTOBEMOREIMPORTANTINACOUSTICRADIATIONTHANTHEDISCITSELFTHISISNOTINTUITIVEASTHEDISCHASALARGERSURFACE29,BUTCANBEEXPLAINEDBYINSTANTANEOUSMODESQUEAL4CAUSEDBYPADMODESFORTHEPTMODE,AGAIN,THEN4DISCMODESEEMSTOBETHEDOMINANTANDSTILLACTIVEVIBRATINGPATTERNOFTHEDISCTHISPATTERNISALSOVISIBLEONSIDEA,BUTWITHOUTASSTRONGAPULSATINGCOMPONENTDUETOTHETANGENTIALPADMOTIONASSEENRADIALLYFORPRSIDEBSHOWSTHERADIATIONOFONEHALFOFADIPOLEWITHITSLONGITUDINALAXISINLINEWITHTHETANGENTIALMOVEMENTOFTHEPADTHERADIATIONPATTERNONSIDEDSHOWSADIPOLESIMILARTOTHATVISIBLEFORTHEPRMODEINVIEW2,BUTWITHACHANGEDAXISINACCORDANCEWITHTHECHANGEDMOTIONOFTHEPADFORTHEPROTMODE,THEVIBRATIONOFTHEDISCSHOWSAN5DISCMODEATAROUND5951HZVIEWS1AND2INTABLE4SHOWTHATTHEOUTOFPLANEACOUSTICRADIATIONONSIDESAANDD
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