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1、256IEEETRANSACTIONSONULTRASONICS,FERROELECTRICS,ANDFREQUENCYCONTROL,VOL.38.NO.3,MAY1991TheConstituentEquationsofPiezoelectricHeterogeneousBimorphsJanG.SmitsandWai-shingChoi,StudentMember,IEEEAbstract-Theelectromechanicalcharacteristicsofahetero-filmaredescribed,andamicrophoneemployi
2、ngthiscon-geneouspiezoelectricbendersubjectedtovariouselectricalandstructionisdiscussed.mechanicalboundaryconditionsarediscussedbasedonthere-Denkmann,Nickell,andStickler[4]presentananaly-sultsofthefreebenderanalysis.Themechanicalboundaryconditionsconsideredare:amechanicalmomentMatth
3、eendsisofacylindricallaminateofdifferentmetalsanddisksofthebender,aforceFappliedperpendicularlytothetipofofpiezoelectricmaterialsforuseintelephonicapplica-thebender,andauniformloadpappliedovertheentirelengthtions.Theycalculatethevoltageoutputofthedevicesofthebender.Theconstituentequ
4、ationsofthebenderunderwhentheyaresubjectedtoaharmonicpressure.theseelectromechanicalinfluencesarederivedbycalculatingTodaandOsaka[lo]discussapiezoelectricelectro-theinternalenergyassumingthermodynamicequilibrium.motionaldeviceusingPVF2inamultimorphstructure.Bendingmotionisdescribeda
5、ndrelationsbetweentheI.INTRODUCTIONbendingandvoltagearegiven.IEZOELECTRICBIMORPHSwereaninvention,CraggandTester[1l]discussthepiezoelectricpolymerPwhichwasinconceptfullyexploredbyC.BaldwinPVDF.Theytouchonchargestorageinpolymerdielec-Sawyer[l],butthedoublestrip(bilame)wasalreadytrics,
6、processingofPVDF,stabilityandfinallyitsappli-mentionedbyP.andJ.CurieasisquotedbyKeller12,cationasatelephonetransducer.Comparisonsarein-reference[141inKeller’spaper].Theheterogeneousbi-cludedbetweenthePVDFtransducerandothertelephonemorph,asadeviceisnamedbysomeauthors[3]whenittransduc
7、ers.consistsofapiezeoelectricelementontopofanonpi-Steel,Harrison,andHarper[3]discussthequasistaticezoelectricelement,hasbeeninvestigatedbymanyau-responseofapiezoelectricbimorphmadeofapiezoelec-thors.Wedonotclaimtolistallauthorswhohaveworkedtriclayerjoinedtoanonpiezoelectriclayer.The
8、irinterestonthisdev
