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，thesuperioritymoreobviouswhencomparetothetraditi

2、onaldevices．Butontheotherhand，aswidelyused，moreproblemsexposedtobesolved．Withthegeometrysizesmaller，themechanicalpropertiesofpiezoelectricunitsanddevicesnotscalereductionasweimagine，butgivesoutsomerelationstosize-dependent．Damagecausedbyproductionprocessandservicewearisunavoidably,It

3、isnotarealisticthatwechangeanewdevicesasthedamagehappened．ithasgreatsignificanceforstudyondamage．Alotofpiezoelectricunitsanddevicescansimplifiedtobeammodel，theresearchiscarriedoutaccordingtopiezoelectriclaminatedbeamsfromaspectsasfollows：Westudythenonlineardeformationsofcantileverpie

4、zoelectriclaminatedbeamswithdamageunderelectricfieldandmechanicalforce．Auniformconstitutiverelationcanbeusedtodescribenonlinearvibrationanalysisofthepiezoelectriclaminatedbeamwhenweconsideredsizeeffectanddamageeffect．BasedonthetheoryofcontinuummechanicsandtheEuler—bernoullitheory，the

5、dynamiccontrolequationexpressionofthecantileverpiezoelectriclaminatedbeamswasdeduced．ByusingGalerkin’Smethod，wetranslatethecontrolequationintononlinearordinarydifferentialequations，theresponsesofthesystemareobtainedthroughnumericalintegrationmethod．Thenwediscusstheresultsbe．tweenwhen

6、theeffectofgeometricnonlinearityisconsideredandbeenneglected，theresultsbetweendifferentcontrolvoltage．Weobtainaseriesofcriticalpull-involtageaswesetthedifferentlengthorthedifferentdamageparameter．Nextweusefiniteelementmethodforsolvingandcomparedtheresultsofthetwogroups．Throughcompari

7、ng，itisfoundthatasthecontrolvoltageincreaseorthedamageincreasethecriticalpull—involtagedecrease．WhencomparetotheNormalbeam，thepull-involtageislow．Finally，somechallengesarepointedout．WhencomparedthetwodifferentMethods，theansysresultsiSlowunderthesamecondition．Theharmonicbalancetechniq

8、ueisusedfors