Research Article Modeling and Analysis of a Piezoelectric Energy Harvester with Varying Cross-Sectional Area Maiara Rosa and Carlos De Marqui Junior Department of Aeronautical Engineering, Engineering School of S˜ ao Carlos, University of S˜ ao Paulo, Avenida Trabalhador S˜ ao-Carlense, 400 Pq Arnold Schimidt, 13566-590 S˜ ao Carlos, SP, Brazil Correspondence should be addressed to Carlos De Marqui Junior; demarqui@sc.usp.br Received 12 July 2013; Accepted 3 March 2014; Published 9 September 2014 Academic Editor: Miguel M. Neves Copyright © 2014 M. Rosa and C. De Marqui Junior. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. his paper reports on the modeling and on the experimental veriication of electromechanically coupled beams with varying cross- sectional area for piezoelectric energy harvesting. he governing equations are formulated using the Rayleigh-Ritz method and Euler-Bernoulli assumptions. A load resistance is considered in the electrical domain for the estimate of the electric power output of each geometric coniguration. he model is irst veriied against the analytical results for a rectangular bimorph with tip mass reported in the literature. he experimental veriication of the model is also reported for a tapered bimorph cantilever with tip mass. he efects of varying cross-sectional area and tip mass on the electromechanical behavior of piezoelectric energy harvesters are also discussed. An issue related to the estimation of the optimal load resistance (that gives the maximum power output) on beam shape optimization problems is also discussed. 1. Introduction he interest in converting vibrations into usable electrical energy has increased over the past years [1–5]. Vibration based energy harvesting is particularly useful for wireless sensor nodes and remotely operated systems with limited energy source. he aim is to provide electrical energy for such systems by using the vibrations available in their environment. Although diferent transduction mechanisms can be used to convert vibrations into electricity, the recent literature shows that piezoelectric transduction has drawn the most attention [1, 3, 5]. he literature on piezoelectric energy harvesting includes diferent models to represent the behavior of electromechan- ically coupled harvesters. Such models range from lumped parameter models [6, 7] to Rayleigh-Ritz type approximate distributed parameter models [7–9] as well as analytical distributed parameter solution attempts [10, 11]. he analyt- ical distributed parameter solutions for unimorph [12] and bimorph [13] piezoelectric energy harvester conigurations with closed-form expressions have been presented. he convergence of the Rayleigh-Ritz type electromechanical solution [7, 9] to the analytical solution given by Erturk and Inman [12] was reported by Elvin and Elvin [14] when a suicient number of admissible functions were used. he investigation into alternative conigurations of elec- tromechanical beams has also been reported in the literature. Erturk et al. [15] presented a linear distributed parameter model for predicting the electromechanical behavior of an L-shaped piezoelectric energy harvester coniguration. A broadband harvester can be obtained when the irst two natural frequencies of the L-shaped beam are properly tuned. he use of tapered cantilevers in order to improve the elec- tromechanical behavior of piezoelectric energy harvesters has also been investigated [16–22]. he shape is changed from the basic rectangular coniguration towards a tapered or reversed tapered geometry and the main motivation is to increase the electrical power output. he modeling of electromechanically coupled beams with nonuniform width is presented in Dietl and Garcia [21]. An optimal beam shape is determined by Hindawi Publishing Corporation Shock and Vibration Volume 2014, Article ID 930503, 9 pages http://dx.doi.org/10.1155/2014/930503