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1、华中科技大学硕士学位论文AbstractTwo-dimensionalmodelsabouttheattachedsubstanceorstructuretostudythedynamiccharacteristicsofacompoundquartzcrystalresonator(QCR)systemareestablishedinthispaper,whilethecompoundsystemconsistsofaquartzcrystalresonatorandarraysofmicro-beams.Thegoverningequationsofm
2、icro-beamsarederivedfromtheEuler-Bernoullibeamtheory,TimoshenkobeamtheoryandthemodifiedEulerbeamtheorywhentakingintoaccountthefirst-orderstraingradient.TheinfluenceofphysicalandgeometricalparametersonfrequencyshiftofQCRsystemisstudiedbyusingtheestablishedmodel.Someusefulresultsare
3、obtained,andfinallythephysicalimplicationisanalyzedindetail.NumericalresultsshowthattheresonancefrequencyofthecompositeQCRsystembecomespositiveornegativewithgraduallychangeofphysicalandgeometricalparametersofeachbeamunit.Andjumppointwilloccurbetweentwoadjacentcycles.Byfurthersolvi
4、ngthenaturalfrequencyofthejumppointsoftheattachedbeamswecanfindthat,thenaturalfrequencyofthebeamsisjustequaltothevibrationfrequencyofQCR,whichimpliesresonance.Besides,itcanbealsofoundthat,whentheelasticmodulesoftheattachedmicrobeamsbecomelargeenough,theperiodiccharacterdisappearsa
5、ndtheattachedlayeronlydecreasesthefrequency.Thereasonforthisphenomenonisthat,whenfixedtheotherparametersandtheelasticmodulesincreasestoacertaindegree,thenaturalfrequencyofthemicrobeamsispositivelygreaterthanthevibrationfrequencyoftheresonator,andtheresonancecannotoccur.Inthiscase,
6、theattachedmicrobeamarrayscanbeequivalenttoarigidqualitylayers.So,theresonantfrequencyofthesystemisalwaysdecreasedandthesolutionsatisfiestheSauerbreyequation.Thissolutionexaminesthevalidityofthemodelestablishedinthispaper.Andinhigh-ordervibrationmodes,theresultsolvedbySauerbreymod
7、elwillnolongerbecorrect.So,thisisasupplementtoSauerbreymodel.Thenweanalyzetheeffectofsheardeformationonfrequencyshiftbetweensurfacemicrobeamsandquartzresonator.Sheardeformationhascertaininfluenceonfrequencyshiftbycomparedwiththepreviousresults,andtheinfluenceisII华中科技大学硕士学位论文moreob
8、viousinthehigherordervibrationmod
