具损伤微纳米结构的非线性动力学分析

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1、硕士学位论文AbstractPiezoelectricmaterial，asanewtypeofmaterials，hasbeenappliedtoallkindsofindustry．Thecommonuseofpiezoelectricunitsanddevicespromotethematureofprocesstechnology．Asthedegreeofthebatchprocesshigher，thepriceofsingledevicecheaper，thesuperioritymoreob

2、viouswhencomparetothetraditionaldevices．Butontheotherhand，aswidelyused，moreproblemsexposedtobesolved．Withthegeometrysizesmaller，themechanicalpropertiesofpiezoelectricunitsanddevicesnotscalereductionasweimagine，butgivesoutsomerelationstosize-dependent．Damag

3、ecausedbyproductionprocessandservicewearisunavoidably,Itisnotarealisticthatwechangeanewdevicesasthedamagehappened．ithasgreatsignificanceforstudyondamage．Alotofpiezoelectricunitsanddevicescansimplifiedtobeammodel，theresearchiscarriedoutaccordingtopiezoelect

4、riclaminatedbeamsfromaspectsasfollows：Westudythenonlineardeformationsofcantileverpiezoelectriclaminatedbeamswithdamageunderelectricfieldandmechanicalforce．Auniformconstitutiverelationcanbeusedtodescribenonlinearvibrationanalysisofthepiezoelectriclaminatedb

5、eamwhenweconsideredsizeeffectanddamageeffect．BasedonthetheoryofcontinuummechanicsandtheEuler—bernoullitheory，thedynamiccontrolequationexpressionofthecantileverpiezoelectriclaminatedbeamswasdeduced．ByusingGalerkin’Smethod，wetranslatethecontrolequationintono

6、nlinearordinarydifferentialequations，theresponsesofthesystemareobtainedthroughnumericalintegrationmethod．Thenwediscusstheresultsbe．tweenwhentheeffectofgeometricnonlinearityisconsideredandbeenneglected，theresultsbetweendifferentcontrolvoltage．Weobtainaserie

7、sofcriticalpull-involtageaswesetthedifferentlengthorthedifferentdamageparameter．Nextweusefiniteelementmethodforsolvingandcomparedtheresultsofthetwogroups．Throughcomparing，itisfoundthatasthecontrolvoltageincreaseorthedamageincreasethecriticalpull—involtaged

8、ecrease．WhencomparetotheNormalbeam，thepull-involtageislow．Finally，somechallengesarepointedout．WhencomparedthetwodifferentMethods，theansysresultsiSlowunderthesamecondition．Theharmonicbalancetechniqueisusedfors