机械专业毕业设计外文翻译相关外文文献概要.docx

机械专业毕业设计外文翻译相关外文文献概要.docx

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机械专业毕业设计外文翻译相关外文文献概要

JiashiYangDepartmentofEngineeringMechanics,

UniversityofNebraska,

Lincoln,NE68588-0526

e-mail:

jyang1@unl.eduAReviewofaFewTopicsinPiezoelectricity

Thisisareviewarticleonafewspecialtopicsinpiezoelectricity:

gradientandnonlocaltheories,fullydynamictheorywithMaxwellequations,piezoelectricsemiconductors,andmotionsofrotatingpiezoelectricbodies.Theyallrequiresomeextensionoftheclassicaltheoryofpiezoelectricity.Theyarerelativelynew,moreadvanced,andgrowingsubjectswithapplicationsorpotentialapplicationsinvariouselectromechanicaldevices.Thearticlecontains209references.（InmemoryofRaymondD.Mindlin（1906–1987.

͓DOI:

10.1115/1.2345378͔

1Introduction

Electroelasticmaterialsexhibitelectromechanicalcoupling.Theyexperiencemechanicaldeformationswhenplacedinanelec-tricfield,andbecomeelectricallypolarizedundermechanicalloads.Strictlyspeaking,piezoelectricityreferstolinearelectrome-chanicalcouplingsonly.Electrostrictionmaybethesimplestnon-linearelectromechanicalcouplinginwhichthemechanicalfieldsdependontheelectricfieldsquadraticallyinthesimplestdescrip-tion.Piezoelectricmaterialshavebeenusedforalongtimetomakemanyelectromechanicaldevices.Examplesincludetrans-ducersforconvertingelectricenergytomechanicalenergyorviceversa,resonatorsandfiltersforfrequencycontrolandselectionfortelecommunicationandprecisetimekeepingandsynchronization,andacousticwavesensors.Thesearemostlyresonantdevicesoperatingwithaparticularmodeofavibratingpiezoelectric.Vi-brationsofapiezoelectricbodywerereviewedinDokmeci͓1͔.Areviewonthehigher-ordertheoriesofpiezoelectricplatesforhighfrequencyvibrationsandapplicationsinpiezoelectricresonatorswasgivenbyWangandYang͓2͔.Effectsofinitialfieldsinelec-troelasticmaterialswithapplicationsinfrequencystabilityofpi-ezoelectricresonatorsandacousticwavesensorsweresumma-rizedanddiscussedinYangandHu͓3͔.Therelativelyrecentdevelopmentofsmartstructurespresentsmanynewapplicationsofpiezoelectricmaterials.Afewreviewarticlesontheapplicationofpiezoelectricmaterialsinsmartstructureshavealreadyap-peared͑RaoandSunar͓4͔,SunarandRao͓5͔,Cheeetal.͓6͔,andTanietal.͓7͔͒.

Likethetwopreviousreviewsbytheauthor͑WangandYang͓2͔,YangandHu͓3͔͒,thisarticleisalsoheavilyinfluencedbytheworkofMindlinandhisstudents.DuringWorldWarIIMindlinservedthegovernmentattheAppliedPhysicsLaboratoryofJohnsHopkinsUniversitywhereheledateamwhichdesignedthefiringelementofthefirstproximityfuse,averyimportantdeviceinthewar.Withtheproximityfuse,theshellsofanti-aircraftgunsdonotneedtobeincontactwithanairplanetoexplodeandbringtheplanedown.Thesuccessrateofanti-aircraftgunswasthenraisedbythousandsoftimes.ForthedevelopmentoftheproximityfuseMindlinwasawardedthePresidentialMedalforMeritin1946.AfterthewarMindlinenteredthefieldofvibrationsofpiezoelec-triccrystals͑resonators͒duetotheneedsoftheBellLaboratoryandtheU.S.Army,andneverleftit.Intheapplicationsofpiezo-electricmaterialsintelecommunicationandfrequencycontrol,theproblemsareusuallydynamicinwhichfrequencyandwavespeedareofprimaryinterest,notstressandstrainforstrengthandfail-ureanalysis.Bothsurfaceacousticwaves͑SAWs͒andbulkacous-ticwaves͑BAWs͒areusedintheseapplications.ForBAWde-vices,theyoftenoperatewiththeso-calledhighfrequencymodes.Takeaplateasanexample.Thehighfrequencymodes,e.g.,thicknessshearandthicknessstretch,arethosemodeswhosefre-quenciesaremainlydeterminedbytheplatethickness,ascom-paredtothelowfrequencymodesofextensionandflexureinstructuralengineeringwhosefrequenciesaremainlydeterminedbythelengthand/orwidthoftheplate.Thestudyofvibrationcharacteristicsofresonantpiezoelectricdevices͑seetherefer-encesinWangandYang͓2͔͒andtheirfrequencystability͑seethereferencesinYangandHu͓3͔͒byMindlinandhisstudentsad-vancedgreatlytheknowledgeonelectromechanicalinteractionsinelectroelasticbodies.MostoftheworkofMindlin’sschoolonpiezoelectricdeviceswaspresentedattheIEEEAnnualFre-quencyControlSymposiaandUltrasonicsSymposia,andwastoalargedegreenotknowntothemechanicscommunity.Thetwopreviousreviews͑WangandYang͓2͔,YangandHu͓3͔͒helpedthecommunicationbetweenpeopleworkingonpiezoelectricityinIEEEandinmechanics.Itishopedthatthisarticlewillservethesamepurpose.

Inthisarticleafewspecialeffectsinpiezoelectricmaterialsarereviewed.Comparedtothelonghistoryofpiezoelectricitysincethediscoveryoftheeffectin1880,thetopicsreviewedinthisarticlearerelativelynew,moreadvanced,andgrowingsubjectswithapplicationsorpotentialapplicationsinvariouselectrome-chanicaldevices.Theyallrequiresomeextensionsoftheclassicaltheoryofpiezoelectricity.Thisincludesgradientandnonlocalef-fects,fullydynamiceffectsgovernedbyMaxwellequations,ef-fectsofsemiconduction,andeffectsofangularmotiononwavesandvibrations.Mindlinwasthefirsttointroducepolarizationgra-dientintothecontinuumdescriptionofpiezoelectricmaterials.Amongmechanicsresearchers,MindlinwasoneoftheearliesttostudythedynamiceffectsfromMaxwellequationsinpiezoelec-tricmaterials.H.F.Tiersten,oneofMindlin’searlystudents,for-mulatedanonlineartheoryforsemiconductioninelectroelasticmaterialsasearlyas1975.TheauthorofthisarticlefollowedMindlin’sstudentsforhisPh.D.andoneofhispostdoctoralstud-ies,andbeganhisresearchonwavesandvibrationsofrotatingpiezoelectricbodiesforangularratesensorapplicationswhenem-ployedbyMotorola,Inc.The100thanniversaryofMindlin’sbirthishere.Thisarticleisanaturaldedicationtotheoccasion.

2GradientandNonlocalEffects

Itiswellknownthatgradienttheoriescandescribesizeeffectswhichareimportantinsmallscaleproblems.Theyalsohaveim-portantconsequencesinproblemswithsingularitieslikeconcen-tratedsourcesanddefects,andcandescribesurfaceandboundarylayerphenomena.Gradienttheoriesareclosertomicroscopictheorieslikelatticedynamicsthanclassicalcontinuumtheories.Theyarestillapplicablewhenthecharacteristiclengthofaprob-lemissosmallthatclassicalcontinuumtheoriesbegintofail.Straingradienttheoriesaretheoldestgradienttheoriesandarenotourmaininteresthere.Thissectionismainlyoneffectsofgradi-entsofelectricvariables.Thedevelopmentofnewtechnologyresultsinverythinelectromechanicalfilmsandverysmallelec-tronicdevices.Thestudyofthesesmalldevicespresentsnewproblemsthatclassicaltheoriesmaynotbeabletodescribe.Theo-

TransmittedbyAssoc.EditorS.Adali.

AppliedMechanicsReviewsNOVEMBER2006,Vol.59/335

Copyright©2006byASME

rieswithgradienteffectsofelectricvariablesmayallowustogofurtherintheseproblemsthantheclassicaltheories.

2.1PolarizationGradient.Forelasticdielectricstherearetwoformulations.Oneusestheelectricpolarizationvectorastheindependentelectricconstitutivevariable͑Toupin͓8͔͒.Theotherusestheelectricfieldvector͑Tiersten͓9͔͒.Mindlin͓10͔extendedthelinearversionofthepolarizationformulationbyallowingthestoredenergydensity⌺todependonthepolarizationgradientPi,j,inadditiontothepolarizationvectorPiandthestraintensorSij:

⌫͑ui,Pi,␾͒=͵V

͚ͫ͑Sij,Pi,Pj,i͒−12␧0␾,i␾,i+␾,iPiͬdV

Sij=͑ui,j+uj,i͒/2͑1͒whereuiisthedisplacementvector,␾theelectricpotential,and␧0thepermittivityoffreespace.Thesummationconventionforrepeatedtensorindicesandtheconventionthatanindexfollowingacommadenotespartialdifferentiationwithrespecttothecoor-dinateassociatedwiththeindexarefollowed.Thestationarycon-ditionoftheabovefunctionalforindependentvariationsofui,␾andPiis

Tji,j=0

−␧0␾,ii+Pi,i=0

Ei+Eji,j−␾,i=0͑2͒where

Tij=ץ͚

ץSij,Ei=−

ץ͚

ץPi,Eij=

ץ͚

ץPj,i

͑3͒

Equation͑2͒representssevenequationsforuiPi,and␾.IfthedependenceonPi,jinEq.͑1͒isdropped,onlyEq.͑2͒1,2willresult,whicharetheequationsoflinearpiezoelectricitywiththeintroductionofDi=−␧0␾,i+Pi.

Mindlin’spolarizationgradienttheoryissupportedbylatticedynamics͑Mindlin͓11,12͔,Askaretal.͓13͔͒.Itrepresentsthelongwave,low-frequencylimitofthefinitedifferenceequationsforalatticeofshell-modelatoms.

WhatmotivatedMindlintostudytheeffectsofpolarizationgradientwasthecapacitanceofaverythindielectricfilm.Experi-mentsshowedthatthecapacitanceofaverythinfilmissystem-aticallysmallerthantheclassicalprediction.Usinghispolariza-tiongradienttheory,Mindlin͓11͔showedthatwhenthefilmthicknessbecomescomparabletoamaterialparameterinthegra-dienttheory,whichhasthedimensionofalengthandcanberelatedtoamicroscopicinteractiondistance,thegradientsolutioncancapturethetrendofthedeviationfromtheclassicalpredic-tion.Healsoshowedthatthepolarizationgradientsolutionofthinfilmcapacitanceagreeswiththepredictionfromlatticedynamics.Mindlin͓14͔alsostudiedtheelectricpotentialofapointcharge.Theclassicalsolutiondivergesatthepointcharge.Thisisbecauseatapointveryclosetothecharge,thechargecannolongerbeconsideredasapointchargeanditsdistributionhastobetakenintoconsideration.Thegradienttheoryyieldsasolutionthatdif-fersfromtheclassicalsolutiononlyatthecloserangeofthesourcepoint,andisvalidatacloserdistancetothesourcepointthantheclassicalsolution.Mindlin͓15͔showedthatinamaterialwithcentrosymmetrywithoutpiezoelectriccoupling,linearelec-trome