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    nonlinearpiezoelectricbehaviorofceramicbendingmodeactuatorsunderstrongelectricfieldsJOURNALOFAPPLIEDPHYSICSVOLUME86,NUMBER615SEPTEMBER1999NonlinearpiezoelectricbehaviorofceramicbendingmodeactuatorsunderstrongelectriceldsQing-MingWang,a)QimingZhang,BaominXu,RuibinLiu,andL.EricCrossIntercollegeMaterialsResearchLaboratory,ThePennsylvaniaStateUniversity,UniversityPark,Pennsylvania16802-4801Received18December1998;acceptedforpublication9June1999Thenonlinearelectromechanicalbehaviorofcantileveredpiezoelectricceramicbimorph,unimorph,andreducedandinternallybiasedoxidewaferactuatorsisstudiedinawideelectriceldandfrequencyrange.Itisfoundthatunderquasistaticcondition,linearrelationshipsbetweenactuatortipdisplacement-electriceld,andblockingforce-electriceldareonlyvalidunderwea……