resonant frequency of an adjustable helmholts resonator in a hydraulic system英文文献资料

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1、ArchApplMech(2009)79:11151125DOI10.1007/s00419-008-0279-5ORIGINALLariKelaResonantfrequencyofanadjustableHelmholtzresonatorinahydraulicsystemReceived:10April2008/Accepted:18November2008/Publishedonline:16December2008©Springer-Verlag2008AbstractAnadjustableHelmholtzresonatorinhydraulicsisstudi

2、edbecauseofobviouslackofstudiesinthefield.FirstthetheoryofaHelmholtzresonatorisreviewedbyexaminingolderstudiesonthesubject.MostofthepreviousstudieshavecoveredHelmholtzresonatorsinacoustics,butthesamebasictheorycanbeappliedtohydraulics.Afterthetheoryreviewthetestequipmentandmeasurementmethodsa

3、representedandsomeresultsarecalculatedanalyticallyusingtheclassicalmodelandamodifiedmodelthattakestheeffectofspringmassintoconsideration.Thespringmassistakenintoaccountbecausethedensityofhydraulicoilisover700timesgreaterthanthedensityofair.Inthelastsectiontheresultsofthecalculationsandmeasure

4、mentsarediscussed,anditisnotedthattheresultsoftheexperimentsagreebetterwiththemodifiedmodelofclassicalHelmholtztheory.Someexplanationsforresidualdiscrepanciesaregivenbutalsosomeremarksarepresented.KeywordsHelmholtzresonator·Hydraulics·Resonance1IntroductionTheaimofthestudywastolearntodefinethe

5、resonantfrequencyofaHelmholtzresonatorinahydraulicsystemsothatitcanbeusedasadamperofacertainfrequency,cf.springmassdampersinmechanics.AtheoryreviewwasconductedinacousticsbecauseonlyafewstudiesaboutHelmholtzresonatorsinhydraulicscanbefound.Thetheoryreviewwassupportedbyanalyticalcalculationand

6、finally,byverificationmeasurements.Figure1presentsasimpleexampleofaHelmholtzresonatorandasingle-degree-of-freedomsystemthatisanalogoustoaHelmholtzresonator.AHelmholtzresonatoriscomposedofacavitythatisconnectedtothesurroundingsthroughanarrowneckorthroughanopening[1,6,10](Fig.1).IfaHelmholtzreso

7、natoriscomparedwithaspringmasssystem,theneckcorrespondstothemassandthecavitywiththespring,asseeninFig.1.ThefluidintheneckhasatotaleffectivemassM[20]M=ρ
0Anln=ρ0An(ln+α)(1)whereρ0isthedensityofthefluid,Anisthecross-sectionalareaoftheneck,ln
istheeffec