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1、ADistributedParameterElectromechanicalModelforCantileveredPiezoelectricEnergy1A.ErturkCenterforIntelligentMaterialSystemsHarvestersandStructures,DepartmentofMechanicalEngineeringCantileveredbeamswithpiezoceramiclayershavebeenfrequentlyusedaspiezoelectricandDepartmentofEngineeringSciencevibratione
2、nergyharvestersinthepastfiveyears.TheliteratureincludesseveralsingleandMechanics,degree-of-freedommodels,afewapproximatedistributedparametermodelsandevenVirginiaTech,someincorrectapproachesforpredictingtheelectromechanicalbehaviorofthesehar-Blacksburg,VA24061vesters.Inthispaper,wepresenttheexactan
3、alyticalsolutionofacantileveredpiezo-e-mail:erturk@vt.eduelectricenergyharvesterwithEuler–Bernoullibeamassumptions.TheexcitationoftheharvesterisassumedtobeduetoitsbasemotionintheformoftranslationintheD.J.Inmantransversedirectionwithsmallrotation,anditisnotrestrictedtobeharmonicintime.CenterforInt
4、elligentMaterialSystemsTheresultingexpressionsforthecoupledmechanicalresponseandtheelectricaloutputsandStructures,arethenreducedfortheparticularcaseofharmonicbehaviorintimeandclosed-formDepartmentofMechanicalEngineering,exactexpressionsareobtained.Simpleexpressionsforthecoupledmechanicalresponse,
5、VirginiaTech,voltage,current,andpoweroutputsarealsopresentedforexcitationsaroundthemodalBlacksburg,VA24061frequencies.Finally,themodelproposedisusedinaparametriccasestudyforauni-morphharvester,andimportantcharacteristicsofthecoupleddistributedparametersystem,suchasshortcircuitandopencircuitbehavi
6、ors,areinvestigatedindetail.Modalelectromechanicalcouplinganddependenceoftheelectricaloutputsonthelocationsoftheelectrodesarealsodiscussedwithexamples.DOI:10.1115/1.2890402Keywords:energyharvesting,piezoelectricity,electromechanicalmodeling,strainnodes1Introductionelingoftheseharvesters.Areliab
7、lemathematicalmodelmayal-lowstudyingdifferentaspectsofenergyharvesting,predictingtheForthepastÞveyears,therehasbeenanexplosionofresearchelectricaloutputs,and,moreover,optimizingtheharvesterfortheintheareaofharvestingen
