哈工程振動(dòng)噪聲-第7章 機(jī)械噪聲的分析測(cè)量和控制

Chapter7NoiseAnalysis,Measurement,andControl第7章機(jī)械噪聲的分析測(cè)量和控制Theroot-meansquare(rms)soundpressure

Combinedsoundpressureofp1andp2Chapter7NoiseAnalysis,Measurement,andControl7.1CombinationofSoundLevels(1)兩列頻率相同且以恒定相位差相交的單頻率噪聲聲波的疊加

相干波：頻率相同、相位差固定不變的波稱為相干波。Chapter7NoiseAnalysis,Measurement,andControl7.1CombinationofSoundLevelsifif這兩種情況下的平均聲能密度分別為Chapter7NoiseAnalysis,Measurement,andControl7.1CombinationofSoundLevels(2)兩列不相干噪聲聲波的疊加orthefrequencyissame,butthephaseanglevariationisofrandomTimeislongenough兩列具有不同頻率，或頻率相同但相交時(shí)相位差無規(guī)律變化的噪聲聲波疊加后的合成聲場，其平均聲能量密度等于每列噪聲聲波平均能量密度之和，這兩列噪聲波稱為不相干波，它們的合成聲場將遵守“能量相加法則”。Chapter7NoiseAnalysis,Measurement,andControl7.1CombinationofSoundLevelsNoiseisemittedusuallyfrommorethanonesourceoratdifferentfrequencies,anditisnecessarytocalculatethecumulativeoroverallsoundlevels.Obviously,sincethesoundlevelscalesarelogarithmic,theycannotbeaddedalgebraically.Combiningofsoundlevelsmaybeperformedusingtheenergyadditiontheoremandtheoveralllevel

L(OA)isdeterminedbyHere,eachsoundleveltobecombinedmightbethenoisefromnindividualsourcesorthesoundlevelsassociatedwithnoctavebands.Theymaybesoundpowerlevelsorsoundpressurelevels.Chapter7NoiseAnalysis,Measurement,andControl7.1CombinationofSoundLevelsChapter7NoiseAnalysis,Measurement,andControl7.1CombinationofSoundLevelsChapter7NoiseAnalysis,Measurement,andControl7.1CombinationofSoundLevels設(shè)有n個(gè)不同頻率，或頻率相同但相位差無規(guī)律變化的噪聲源，則其平均聲壓級(jí)可推導(dǎo)得到L1-L2012345678910Lc-L13.02.52.11.81.51.21.00.80.60.50.4Anothereasyandusefulmethodforcombiningsoundlevelsistoutilizethetableasbellow.Thecombinedeffectofsoundsdependsonthedifferenceintheirdecibellevels.實(shí)際計(jì)算表明，兩列聲壓級(jí)相同的噪聲疊加后，總聲壓級(jí)僅增加3dB；兩列噪聲的聲壓級(jí)相差10dB以上，則聲壓級(jí)低的那列噪聲對(duì)總聲壓級(jí)的貢獻(xiàn)可以忽略不計(jì)，總聲壓級(jí)近似等于聲壓級(jí)高的那個(gè)值.Chapter7NoiseAnalysis,Measurement,andControl7.1CombinationofSoundLevels(1)OctaveBandand1/3OctaveBandSpectralAnalysis

Innoisecontrolengineering,thebandsarerelatedbythefollowingrelationshipn=1,octaveband

n=1/3,one-third-octaveband

ThecenterfrequencyofanysuchbandisdefinedasthegeometricmeanThelowerandupperlimitfrequenciesmaybedeterminedfromthecenterfrequencyasChapter7NoiseAnalysis,Measurement,andControl7.2SpectralAnalysisofNoiseOctaveBand1/3OctaveBandLowerLimitFrequency(Hz)CenterFrequency(Hz)UpperLimitFrequency(Hz)LowerLimitFrequency(Hz)CenterFrequency(Hz)UpperLimitFrequency(Hz)2231.54422.42528.228.231.535.535.54044.744638844.75056.256.26370.870.880891100112112125141141160178177250355178200224224250282282315355355500710355400447447500562562630708Chapter7NoiseAnalysisandMeasurement7.2SpectralAnalysisofNoise7101,0001,4207088008918911,0001,1221,1221,2501,4131,4202,0002,8401,4131,6001,7781,7782,0002,2392,2392,5002,8182,8404,0005,6802,8183,1503,5483,5484,0004,4674,4675,0005,6235,6808,00011,3605,6236,3007,0797,0798,0008,9138,91310,00011,22011,36016,00022,72011,22012,50014,13014,13016,00017,78017,78020,00022,390Chapter7NoiseAnalysisandMeasurement7.2SpectralAnalysisofNoise(1)OctaveBandand1/3OctaveBandSpectralAnalysis

BandNumber12345678CenterFreq.(Hz)631252505001000200040008000SPLat3ft(dB)1261321281191151089890

133134.3134.4OverallSPL

134dBChapter7NoiseAnalysisandMeasurement7.2SpectralAnalysisofNoise128.5115.898.6115.9L1-L2012345678910Lc-L13.02.52.11.81.51.21.00.80.60.50.4Chapter7NoiseAnalysisandMeasurement7.2SpectralAnalysisofNoise(2)ConstantBandwidthNarrowBandSpectralAnalysis在倍頻程分析中，中心頻率越高，對(duì)應(yīng)的帶寬越大，得出的數(shù)據(jù)越粗糙。在恒定窄帶分析中，在高頻域仍能保持同樣的帶寬，可達(dá)到很高的分析精度。但其代價(jià)是大大增加了分析的工作量。Ifthenoisehasfrequenciesevenlydistributedthroughouttheaudiblefrequencyrangeitisknownaswhitenoise.Chapter7NoiseAnalysisandMeasurement7.2SpectralAnalysisofNoiseFrequency(Hz)Relativeresponse(dB)Frequency(Hz)Relativeresponse(dB)2531.540-44.7-39.4-34.68001,0001,250-0.80+0.6506380-30.2-26.2-22.51,6002,0002,500+1.0+1.2+1.3100125160-19.1-16.1-13.43,1504,0005,000+1.2+1.0+0.5200250315-10.9-8.6-6.66,3008,00010,000-0.1-1.1-2.5400500630-4.8-3.2-1.912,50016,00020,000-4.3-6.6-9.3Aelectricalweightingnetworksforsoundlevelmeter

Chapter7NoiseAnalysisandMeasurement7.3WeightedSoundLevelsBandNumber12345678CenterFreq.(Hz)631252505001000200040008000SPLat3ft(dB)1261321281191151089890A-weighting-26.2-16.1-8.6-3.2+0+1.2+1.0-1.1A-weightedSPL99.8115.9119.4115.8115109.29988.911612111699.4

122.2116.1

123.2OverallA-weightedSPL

123dB(A)Chapter7NoiseAnalysisandMeasurement7.3WeightedSoundLevelsHomeWorks距離發(fā)動(dòng)機(jī)3米處測(cè)得的1/3倍頻程聲壓級(jí)列于表A，試畫出倍頻程頻譜圖，并計(jì)算總的A聲壓級(jí)。頻率(Hz)506380100125160200250SPL(dB)10898113119120115110112頻率(Hz)315400500630800100012501600SPL(dB)104102100989910310099頻率(Hz)200025003150400050006300800010000SPL(dB)9794959285787570表A.1/3倍頻程聲壓級(jí)的測(cè)量值Typesofsound-absorbingmaterialsSound-absorbingmaterialsareutilizedinalmostallareasofnoisecontrolengineering.Theporoussound-absorbingmaterialsareavailableintheformofmats,boards,mineralfibers,opencellfoams.Theyhaveopenporeswithtypicaldimensionsbelow1mmthatareverysmallerthanthewavelengthofsound.Here,eachcanbetreatedasalossyhomogeneousmedium.Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.1PorousSound-AbsorbingMaterials（多孔吸聲材料）Fullreticulatedplasticfoam,Partiallyreticulatedplasticfoam,Glassfiber,Mineralwool.Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.1PorousSound-AbsorbingMaterials（多孔吸聲材料）HowporousmaterialsabsorbsoundOwingtotheactingsoundpressure,theairmoleculesoscillateintheinterstices[in’t?:stis](空隙)ofaporousmaterialwiththefrequencyofexcitingsoundwave.Theoscillationsresultinfrictionallosses,andtheyconvertthesoundenergyintoheat.Changesinflowdirectionandexpansionsandcontractionsoftheflowthroughirregularporesresultinlossofmomentuminthedirectionofwavepropagation.

Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.1PorousSound-AbsorbingMaterials（多孔吸聲材料）Physicalpropertiesofporoussound-absorbingmaterialsManyexperimentalstudiesofthebehaviourofcommonsound-absorbingmaterialofwhichthestructuralskeletonsareeffectivelyrigidhasshownthattherearethreegrossparametersthatprincipallycontroltheirsoundabsorptioncharacteristics.

Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.1PorousSound-AbsorbingMaterials（多孔吸聲材料）Porosity（孔隙率）

Porosityisdefinedastheratioofthevolumeofvoidstothetotalvolumeoccupiedbytheporousstructure:itissymbolizedhereinbyh.

whereVgisthevolumeofgasphase,Vsisthevolumeofsolidphase,VmisthevolumeofmaterialChapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.1PorousSound-AbsorbingMaterials（多孔吸聲材料）Porosityρs

isdensityofthesolid(frame)andρmisbulkdensity(容積密度)oftheporousmaterial.Considerafiberglassinsulationproduct:Itisgenerallyinexcessof95%inmineralandglasswoolsandporousplasticfoams.Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.1PorousSound-AbsorbingMaterials（多孔吸聲材料）(2)FlowResistivity(比流阻）whereΔpisthesteadypressuredifferentialacrossahomogeneouslayerofthicknessΔx,νisfacevelocityoftheflowthroughthematerial(actuallyitistheaveragevelocitywithinthematerial).Flowresistivity(specificflowresistance)

σisamostimportantphysicalcharacteristicofaporousmaterial.ItisdefinedasChapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.1PorousSound-AbsorbingMaterials（多孔吸聲材料）(2)FlowResistivityTheflowresistanceofasheetofmaterialofthicknessΔxisgivenbyσΔx.Theflowresistivityofcommonabsorbingmaterialstypicallyliesintherange2×１０３

to2×１０５

Ns/(m4).Foragivenmaterialbulkdensity,flowresistivityincreasesstronglyasfiberdiameterisdecreased.

Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.1PorousSound-AbsorbingMaterials（多孔吸聲材料）(3)StructureFactor（結(jié)構(gòu)因子）Thevariousinfluencesofthegeometricformoftheskeletononeffectivedensityandcompressibilityarelumpedtogetherintoa‘structurefactor’symbolizedbys.Thestructurefactordecreaseswithincreasingfrequencyandrangesfromextremehighvalueofs=6downtos=1butgenerallyfallsintherangeofs=1.3.Mostnumericalcalculationsuses=1.Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.1PorousSound-AbsorbingMaterials（多孔吸聲材料）(1)Themodifiedplanewaveequation

Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.2PlaneWaveSoundPropagationinPorousMaterialswhereκistheeffectivebulkmodulusofthegas.(2)Harmonicsolutionofthemodifiedplanewaveequation

SettingSubstitutingitintothemodifiedwaveequationyields

oriscalledcomplexwavenumber.Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.2PlaneWaveSoundPropagationinPorousMaterials(2)Harmonicsolutionofthemodifiedplanewaveequation

Foraharmonicprogressivewave,.Wewritethecomplexwavenumber,inwhichisthe‘a(chǎn)ttenuationconstant’andisthe‘propagationconstant’.Therefore,thegeneralsolutionofthemodifiedplanesoundwaveequationmaybeexpressedasChapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.2PlaneWaveSoundPropagationinPorousMaterials(2)Harmonicsolutionofthemodifiedplanewaveequation

ThespatialdistributionofinstantaneouspressureisillustratedbythefollowedFigure.Exponentialattenuationofaprogressiveharmonicwave:instantaneouspressuredistributionChapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.2PlaneWaveSoundPropagationinPorousMaterialsACBDx=-t

x=0Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.3LargePlatAbsorbersSoundenergyabsorptioncoefficientwhereEaandEiaretheabsorbedandincidentenergies,respectively,Risthereflectioncoefficientdefinedastheratioofthereflectedandincidentsoundpressureattheinterface.Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.3LargePlatAbsorbersThesoundpressuresandparticlevelocitiesintheairandporousmaterialsareexpressedasAtx=0,theparticlevelocityiszero,yieldsC=D

Where

Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.3LargePlatAbsorbersAtx=-t,thecontinuitiesofsoundpressureandparticlevelocitygive

Combiningaboveexpressions,oneobtainthesoundpressurereflectioncoefficientasSoundabsorptioncharacteristicsoffinitethicklayerofporousmaterial超細(xì)玻璃棉歸一化吸聲系數(shù)曲線Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.3LargePlatAbsorbers下限頻率下半頻帶寬度Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.3LargePlatAbsorbersPrinciplefactorinfluencingsoundabsorptioncharacteristicsoffinitethicklayerofporousmaterial:DensityofmaterialThicknessofmaterial容重增加，低頻吸聲系數(shù)變大，但高頻吸聲系數(shù)降低；容重過大會(huì)使總的吸聲效果明顯降低。一般超細(xì)玻璃棉容重大約可取15～25kg/m3，礦渣棉為120～130kg/m3。如前頁圖，增加吸聲材料厚度會(huì)使材料吸聲系數(shù)曲線向低頻方向移動(dòng)。Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.3LargePlatAbsorbersAirgapbehindthematerial

空氣層的作用相當(dāng)于增加材料厚度，改善低頻吸聲效果。研究表明，當(dāng)空氣層厚度為入射聲波1/4波長的奇數(shù)倍時(shí)，吸聲材料處的聲波質(zhì)點(diǎn)振速最大，吸聲效果最好。當(dāng)空氣層厚度為入射聲波1/2波長的倍數(shù)時(shí)，吸聲材料處的聲波質(zhì)點(diǎn)振速最小，吸聲效果最差。一般取空氣層厚度為7～15cm。Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.3LargePlatAbsorbersPerforatedfacingTemperatureandhumidity

護(hù)面層常用材料：玻璃絲布、塑料窗紗、金屬絲網(wǎng)、穿孔板等。當(dāng)穿孔率大于20%，可以忽略護(hù)面層對(duì)吸聲效果的影響。

溫度高、濕度大都對(duì)吸聲效果有負(fù)面影響。前者使共振頻率向高頻移動(dòng)，后者更是使吸聲系數(shù)降低（材料空隙被水分占據(jù)）。Structuresofabsorbers吸聲尖劈：吸聲尖劈的結(jié)構(gòu)如圖所示，屬于阻抗?jié)u變型結(jié)構(gòu)。室內(nèi)環(huán)境空間中的尖劈用多孔吸聲材料做成，外包玻璃纖維布或金屬絲網(wǎng)。吸聲尖劈具有優(yōu)良的吸聲性能，高于截止頻率的頻段的吸聲系數(shù)均高于0.99。截止頻率的大小由吸聲材料、尖劈總長度及空氣層厚Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.4ResonanceAbsorbers度決定。例如，采用玻璃棉、礦渣棉等優(yōu)質(zhì)吸聲材料制作的尖劈總長度為lm，后留空氣層厚度5一l0cm時(shí)，截止頻率可達(dá)70Hz。因此吸聲尖劈被廣泛地用于消聲室中。b)共振吸聲結(jié)構(gòu)薄板共振結(jié)構(gòu)：薄板共振吸聲結(jié)構(gòu)的結(jié)構(gòu)形式是在周邊固定在框架上金屬板、膠合板等薄板后，設(shè)置一定深度空氣層。由薄板的彈性和空氣層的彈性與板的質(zhì)量形成一個(gè)共振系統(tǒng)，在系統(tǒng)共振頻率附近具有較大的吸聲作用。注意：薄板受擾（氣流、動(dòng)力等）產(chǎn)生的振動(dòng)會(huì)發(fā)出噪聲。而這里薄板共振吸聲結(jié)構(gòu)產(chǎn)生的振動(dòng)是有聲引發(fā)的，消耗聲能量。Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.4ResonanceAbsorbers

穿孔板吸聲結(jié)構(gòu)：這種吸聲結(jié)構(gòu)是在鋼板、膠合板等類薄板上穿孔，并在其后設(shè)置空氣層，必要時(shí)在空腔中加襯多孔吸聲材料。它可以看作是許多亥姆霍茲共振器的并聯(lián)。密封的空腔通過板上的小孔與外界聲場相通?？最i處的空氣柱有如質(zhì)量，空腔內(nèi)空氣有如彈簧，構(gòu)成了彈性振動(dòng)系統(tǒng)。當(dāng)外來聲波頻率等于結(jié)構(gòu)共振頻率時(shí)，將引起孔頸中空氣柱發(fā)生共振，此時(shí)空氣柱的振動(dòng)位移最大，振動(dòng)速度最大，孔壁摩擦損耗也最大，對(duì)聲能的消耗也最大。Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.4ResonanceAbsorbers

薄型塑料盒式吸聲體此類結(jié)構(gòu)是用改性硬質(zhì)PVC材料真空成形高頻焊接加工而成的多層盒體結(jié)構(gòu)，利用封閉盒體的諧振作用達(dá)到吸聲目的。盒體厚度為50mm～100mm，許多盒體連成0.5m×0.5m的板。這種新型的吸聲結(jié)構(gòu)吸聲性能優(yōu)良，物理性能穩(wěn)定，重量輕，透光性好，易于施工，在工礦企業(yè)的噪聲控制中得到廣泛應(yīng)用。Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.4ResonanceAbsorbersc)微穿孔板吸聲結(jié)構(gòu)微穿孔板吸聲結(jié)構(gòu)是在厚度小于1mm的薄板上每平方米鉆上萬個(gè)孔徑小于1mm的微孔，穿孔率控制在1%-5％，將這種板固定在剛性平面之上，并留有適當(dāng)空腔。微穿孔板的聲阻比穿孔板大得多，決定了共振吸聲系數(shù)高，而聲質(zhì)量卻小得多，聲阻與聲質(zhì)量之比大為提高，加寬了吸聲頻帶。Chapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.4ResonanceAbsorbers

a)Resonancefrequencyresonanceabsorbers:式中P為穿孔率，D為穿孔板后空氣層厚度，l為穿孔的有效長度。對(duì)薄板共振結(jié)構(gòu)，共振頻率為式中M為薄板密度，D為空氣層厚度。共振時(shí)的吸聲系數(shù)約為0.2～0.5。MainparametersevaluatingtheresonanceabsorbersChapter7MechanicalNoiseControlTechniques7.4NoiseReductionbySoundAbsorption7.4.4ResonanceAbsorbersb)Soundabsorptioncoefficientattheresonantfrequency式中rA為聲阻率R與空氣特性阻抗ρ0c0之比，稱為相對(duì)聲阻率。c)Effectivebandwidth微穿孔板吸聲結(jié)構(gòu)；串聯(lián)式雙層孔板結(jié)構(gòu)不可能大于1Chapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.1DefinitionsofSoundInsulationThesoundpowertransmissioncoefficientofastructureisdefinedasChapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.1DefinitionsofSoundInsulationTransmissionloss（即所謂隔聲量）maybeexpressedaswhereandaretheincidentandtransmittedsoundintensities,respectively.Generalvariationofthetransmissionlosswithfrequencyforahomogeneouspanel.Chapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

(1)RegionI:Stiffness-ControlledRegionAtlowfrequencies,thepanel(providethatthepanelisverythin)vibratesasawhole,andsoundtransmissionChapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

A1B1A2throughthepanelisdeterminedprimarilybythestiffnessofthepanel.Atthesurfaceofthepanel(foraverythinpanel),theparticlevelocitiesarebothequaltotheinstantaneousvelocityofthepanel.WemaywritethefollowingexpressionsfromaboveEquationsfor:Ifthepanelhasafinitestiffness,thenetforceactingonthepanelisequaltothe“spring-force”ofthepanel.Thespecificmechanicalcomplianceormechanicalcomplianceperunitareawillbedenotedbythesymbol.Chapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

ThesoundpowertransmissioncoefficientfornormalincidencemaybedeterminedThetransmissionlossfornormalincidencemaybewrittenasfollows:whereChapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

Forarectangularpanel,theexpressionforthespecificmechanicalcomplianceisgivenby:Thequantitiesaandbarethewidthandheightofthepanel;histhethicknessofthepanel;andEandaretheYoung’smodulusandPoisson’sratioforthepanelmaterial,respectively.Chapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

ForacircularpanelwithadiameterDandthicknessh,thespecificmechanicalcomplianceisgivenby:

(2)ResonantFrequency

Asthefrequencyoftheincidentwaveisincreased,theplatewillresonateataseriesoffrequencies,calledtheresonantfrequencies.

ThelowestresonantfrequencymarksthetransitionbetweenRegionIandRegionIIbehavior.Theresonantfrequenciesareafunctionoftheplatedimensions.Forarectangularplatehavingdimensionsa×b×hthick,theresonantfrequenciesaregivenby

ThequantitycListhespeedoflongitudinalsoundwavesinthesolidpanelmaterialThequantityisthedensityofthepanelmaterial.Chapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

Usually,thelowestresonantfrequency(thefundamentalfrequency)isthemostpredominantfrequency.Thisfrequencycorrespondstom=n=1Thefundamentalresonantfrequencyforcircularplateisgivenbythefollowingexpressions.ForacircularplateofdiameterDandthicknesshclamped(夾住)attheedgeForacircularplatewithasimplesupportededge,thefundamentalresonantfrequencyisgivenbyChapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

(3)RegionII:Mass-controlledRegion

Chapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

A1B1A3oxAtthefirstinterface(x=0),thepressureinmedium1andthepressureinmedium2areequal,andtheparticlevelocitiesinmediums1and2arealsothesameattheinterface.Usingtheseconditions,wefindthefollowingrelations:Atthesecondinterface(x=h),thepressuresandvelocitiesarealsoequal.Usingthiscondition,weobtainasecondsetofrelationshipsbetweenthecoefficients:Chapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

WemaycombineaboveEquationstoobtaintheratioA1/A3

ThemagnitudeoftheratioA1/A3maybewrittenasorChapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

Ifthematerialsarethesameonbothsidesofthewall,i.e.,Z1=Z3theaboveequationreducestoForthefrequencyrangeofinterestinanalysisoftransmissionofsoundthroughwalls,thetermk2hissmallandZ2＞＞Z1.Chapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

Thetransmissionlossfornormalincidenceisrelatedtothesoundpowertransmissioncoefficientfornormalincidence:Ifweintroducethequantity,calledthesurfacemass,theaboveequationmaybewritteninthefollowingformoftencalledthemasslaw.Chapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

Because

,so(4)CriticalFrequency

Asthefrequencyoftheimpingingsoundwaveincreasesinthemass-controlledregion,thewavelengthofthebendingwavesinthematerial,whicharefrequency-dependentapproachesthewavelengthofsoundwavesintheair.Coincidence(equalityofthewavelengths)firstoccursatgrazingincidence（掠入射）,orforanangleof

incidenceof.Whenthisconditionhappens,theincidencesoundwavesandbendingwavesinthepanelreinforceeachother.Theresultingpanelvibrationcausesasharpdecreaseinthepaneltransmissionloss.ThepointcorrespondstothetransitionfromRegionⅡbehaviortoRegionⅢbehavior.Chapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

ConditionforCoincidence:or

arethewavelengthandpropagationspeedofthebendingwaveinthepanel.Chapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

Thecriticalfrequency(thelowestfrequencyatwhichcoincidencehappens)isgivenbyChapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

Ifwecombineandtheequationabove,wefindthattheproduct(Msfc)isafunctionofthephysicalpropertiesofthepanelandsonicvelocity(c)intheairaroundthepanel.(5)RegionⅢ:Damping-ControlledRegion

Forsoundwavesstrikingthepanelatallangles(randomincidence)atfrequencygreaterthanthecriticalfrequency,thefollowingempiricalfield-incidenceexpressionappliesforthetransmissionlossinthedamping-controlledregionThequantityisthetransmissionlossfornormalincidenceatthecriticalfrequency:isthedampingcoefficientforthepanelmaterial.Chapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

Example

Anoakdoorhasdimensionof0.90mwideby1.80mhighby35mmthick.Theaironbothsidesofthedoorhasatemperatureof20℃,forwhich,,and.Determinethetransmissionlossforthefollowingfrequencies:(a)63Hz,(b)250Hz,and(c)2000Hz.LongitudinalwavespeedDensityCriticalfrequencyproductChapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

DampingfactorYoung’smodulusPoisson’sratioChapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

ThefirstresonantfrequencyisThesurfacemassis:ThecriticalorwavecoincidencefrequencyisChapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

(a)ForthiscaseliesinRegionI,thestiffness-controlledregion.ThespecificmechanicalcompliancemaybeevaluatedThesoundpowertransmissioncoefficientThetransmissionlossforafrequencyof63HzisChapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

(b)FortheoperatingregionisRegionII,themass-controlledregion.ThesoundpowertransmissioncoefficientfornormalincidenceisThetransmissionlossfornormalincidenceisChapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

(c)ForthiscaseliesinRegionIII,thedamping-controlledregion.ThetransmissionlossfornormalincidenceatthecriticalfrequencyisThetransmissionlossforafrequencyof2000HzisChapter7MechanicalNoiseControlTechniques7.5NoiseInsulation7.5.2SoundTransmissionthroughaPanel

Asilencerormufflerisadevicethatallowsthegas/airorliquidpassthroughandcanattenuatethenoise.Classification:Reactive(reflective)Dissipative(absorptive)Combinationreactive/dissipative

Theaerodynamicnoisegeneratedbygas/airconsuming/handlingequipments,suchasinternalcombustionengines,gasturbines,blowers,pumps(vacuumpumporotherpunp),compressorsandfans,iscontrolledthroughtheuseofsilencersandmufflers.Chapter7MechanicalNoiseControlTechniques7.6SilencersandMufflers7.6.1AerodynamicNoiseandSilencersNoiseReductionMechanismandcharacteristicsofReactiveSilencerChapter7MechanicalNoiseControlTechniques7.6SilencersandMufflers7.6.1AerodynamicNoiseandSilencers擴(kuò)張室式消聲器Silencerwithexpansionchambers

共振式消聲器ResonantSilencer干涉型消聲器SilencerbasedonInterferenceprincipleReactivesilencersconsisttypicallyofseveralpipesegmentsthatinterconnectwithanumberoflargerchambers.NoiseReductionMechanismandcharacteristicsofReactiveSilencerChapter7MechanicalNoiseControlTechniques7.6SilencersandMufflers7.6.1AerodynamicNoiseandSilencersTheareadiscontinuityresultsinareflectionofpartofthesoundwavesbacktowardthesource,orbackandforthamongthechambers,preventingthatpartfrombeingtransmittedpastthesilencer.Thereactivesilencersaremoreeffectiveatlowerfrequenciesthanathighfrequencies,andmostwidelyusedtoattenuatetheexhaustnoiseofinternalcombustionengines.NoiseReductionMechanismandcharacteristicsofDissipativeSilencerChapter7MechanicalNoiseControlTechniques7.6SilencersandMufflers7.6.1Aerodynamic