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带质量块微型双稳态压电板的动力学分析 Introduction Piezoelectricmaterialshavebeenusedextensivelyforawiderangeofapplications,suchassensors,actuators,energyharvestingdevices,andresonators,duetotheiruniqueelectromechanicalproperties.Thepropertyofthepiezoelectriceffectallowstheconversionofelectricalenergyintomechanicalmotionandviceversa.Inrecentyears,thedevelopmentofmicro-andnanoscalepiezoelectricdevicesforvariousapplicationshasbeenofgreatinteresttotheresearchcommunity. Onesuchdevicethathasreceivedmuchattentionisthemicrocantileverormicromechanicalresonator.Thesedevicesarecapableofexhibitinglargedisplacementandhighresonantfrequenciesandcanbeusedforsensing,actuation,andresonantfilteringapplicationsinthemicroandnanoscale.Inparticular,thedoublyclampedmicrocantileverwithamassattachedatthefreeendhasbeenshowntoexhibitbistablebehavior.Thismeansthatthedevicehastwostableequilibriumpositions,andonceitissetinmotion,itwillstayinoneofthetwostablepositionsuntilperturbed. Dynamicsofmicrocantileverwithamassblock Inthispaper,wepresentadynamicanalysisofadoublyclampedmicrocantileverwithamassblockattachedtothefreeend.Afullanalyticalmodelofthesystemisdeveloped,takingintoaccountthepiezoelectriceffectofthematerial,dampingduetoviscousfluid,andthemassoftheattachedblock.ThegoverningequationofmotionforthesystemisderivedusingtheEuler-Lagrangeequation. Inordertostudythedynamicsofthesystem,anonlineardynamicalanalysisisperformed.Themethodofharmonicbalanceisusedtodeterminetheperiodicsteady-stateresponseofthesystem.Thefrequencyresponsecurvesareplottedfordifferentvaluesofthesystemparameters,suchastheappliedvoltage,theattachedmass,andthedampingcoefficient. Resultsanddiscussion Theresultsobtainedfromtheanalysisrevealthatthesystemexhibitsbistablebehavior,withahysteresisloopinthevoltageversusdisplacementresponsecurve.Thesizeofthehysteresisloopisdependentonthedampingcoefficientandtheattachedmass.Furthermore,thebifurcationbehaviorofthesystemisstudiedinthefrequencyresponsecurves.Thesystemundergoessupercriticalpitchforkbifurcation