An electromechanical finite element model for piezoelectric energy harvester plates Carlos De Marqui Junior a,Ã , Alper Erturk b , Daniel J. Inman c a Department of Aeronautical Engineering, Engineering School of Sao Carlos, University of Sao Paulo, Brazil b Center for Intelligent Material Systems and Structures, Department of Engineering Science and Mechanics, Virginia Tech, USA c Center for Intelligent Material Systems and Structures, Department of Mechanical Engineering, Virginia Tech, USA article info Article history: Received 13 January 2009 Received in revised form 5 May 2009 Accepted 12 May 2009 Handling Editor: C.L. Morfey Available online 11 June 2009 abstract Vibration-based energy harvesting has been investigated by several researchers over the last decade. The goal in this research field is to power small electronic components by converting the waste vibration energy available in their environment into electrical energy. Recent literature shows that piezoelectric transduction has received the most attention for vibration-to-electricity conversion. In practice, cantilevered beams and plates with piezoceramic layers are employed as piezoelectric energy harvesters. The existing piezoelectric energy harvester models are beam-type lumped parameter, approximate distributed parameter and analytical distributed parameter solutions. However, aspect ratios of piezoelectric energy harvesters in several cases are plate-like and predicting the power output to general (symmetric and asymmetric) excitations requires a plate-type formulation which has not been covered in the energy harvesting literature. In this paper, an electromechanicallycoupled finite element (FE) plate model is presented for predicting the electrical power output of piezoelectric energy harvester plates. Generalized Hamilton’s principle for electroelastic bodies is reviewed and the FE model is derived based on the Kirchhoff plate assumptions as typical piezoelectric energy harvesters are thin structures. Presence of conductive electrodes is taken into account in the FE model. The predictions of the FE model are verified against the analytical solution for a unimorph cantilever and then against the experimental and analytical results of a bimorph cantilever with a tip mass reported in the literature. Finally, an optimization problem is solved where the aluminum wing spar of an unmanned air vehicle (UAV) is modified to obtain a generator spar by embedding piezoceramics for the maximum electrical power without exceeding a prescribed mass addition limit. & 2009 Elsevier Ltd. All rights reserved. 1. Introduction The research interest in converting ambient vibration energy to usable electrical energy has increased in the last years [1–5]. The concept of energy harvesting is particularly useful for wireless sensors powered by batteries and remotely operated systems with limited energy source. The goal of the research in vibration-based energy harvesting is to provide electrical energy for such systems by utilizing the vibrations available in their environment. Unmanned air vehicles (UAVs) and micro air vehicles (MAVs) constitute unique application systems where the possibility of an additional energy source is very important. UAVs are designed to maximize the endurance and flight range with the limited energy available in operation. A possible Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jsvi Journal of Sound and Vibration ARTICLE IN PRESS 0022-460X/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsv.2009.05.015 Ã Corresponding author. Tel.: +551633739417; fax: +551633739590. E-mail addresses: demarqui@sc.usp.br (C. De Marqui Junior), erturk@vt.edu (A. Erturk), dinman@vt.edu (D.J. Inman). Journal of Sound and Vibration 327 (2009) 9–25