Response of piezoelectric stack actuators under combined electro-mechanical loading Milan Mitrovic a, * , Greg P. Carman a , Friedrich K. Straub b a Department of Mechanical and Aerospace Engineering, University of California, 48-121 Eng. IV, Los Angeles, CA 90095 USA b Boeing, M30-B346, 5000E. McDowell Road, Mesa, AZ 85215, USA Received 24 August 1999; in revised form 2 June 2000 Abstract The response of six piezoelectric stack actuators under electrical, mechanical, and combined electro-mechanical loadingwasinvestigated.Thefocuswastounderstandthebehaviorofpiezoelectricmaterialsundercombinedelectro- mechanicalloadingscenario,andtodeterminefundamentalpropertiesnecessarytomodeltheconstitutiveresponseand optimize the actuator performance. Parameters that were evaluated include strain output, permittivity, mechanical stiness,energydensity,andcouplingcoecientsasafunctionofmechanicalpreloadandelectric®eldvalues.Results indicate that for certain actuators stiness values change by more than 100% depending on the operating conditions. The magnitude of the applied compressive load signi®cantly in¯uences strain output, electrical and mechanical energy density, and coupling coecients. Initially, the strain output and energy density is enhanced with an increase in me- chanicalpreloadbyasmuchas60%forsomeactuators,withmaximumvaluesoccurringatpreloadsbetween25and40 MPa. A similar trend is observed under combined out-of-phase electro-mechanical loading. However, linear super- position of strain outputs obtained under constant loading tests, does not lead to accurate predictions over the broad rangeofcombinedelectro-mechanicalloadingconditions.Thisindicatesaneedformoreaccurateconstitutiverelations topredictthehighlynon-linearprocessesrelatedtocombinedelectro-mechanicalloading. Ó 2001ElsevierScienceLtd. All rights reserved. Keywords: Piezoelectric stacks; Coupling coecients; Energy density; Electro-mechanical loading 1. Introduction Piezoelectric materials are currently being investigated in a number of actuator applications, including precision positioning, vibration suppression, noise control, and compact hybrid actuator devices Sumali etal.,1992;Chenetal.,1998).Anotherapplicationthathasreceivedconsiderableattentioninrecentyears International Journal of Solids and Structures 38 2001) 4357±4374 www.elsevier.com/locate/ijsolstr * Corresponding author. Tel.: +1-310-825-9564; fax: +1-310-206-4830. E-mail address: milanx@cad.ucla.edu M. Mitrovic). 0020-7683/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII:S0020-768300)00273-0