Modeling and Analysis of a Piezoelectric Energy Harvester with Varying Cross-Sectional Area

This paper reports on the modeling and on the experimental verification of electromechanically coupled beams with varying cross-sectional area for piezoelectric energy harvesting. The 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 configuration. The model is first verified against the analytical results for a rectangular bimorph with tip mass reported in the literature. The experimental verification of the model is also reported for a tapered bimorph cantilever with tip mass. The effects 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.