A problem in piezoelectric bimorph energy harvesting is to generate the most power with limits in system mass. The authors propose a new approach: to change the shape of the beam to concentrate the strain in sections of the beam where it can contribute the most to transduction. A vibration model of beams with non-uniform width is developed and validated with shaker table tests. Three beams with different shapes are tested over a wide band, encompassing the lowest two modes of vibration. An optimal beam shape is calculated using a heuristic optimization code and the attributes of this optimal beam are discussed. Then, beam shapes are optimized to allow for increased base excitation and constrained by maximum root strain. Finally, the tip mass-to-beam mass ratio is studied parametrically, correlating increased transduction with increased beam mass.

Piezoelectric bimorph cantilevered beams are often used as energy harvesting devices. These devices are desired for, among other applications, remote sensing and animal tracking due to their potential for eliminating the need for battery replacement. Existing models of piezoelectric bimorph cantilevered beams have proved to describe the dynamics of slender beams at high frequencies accurately. In this paper, a Timoshenko model of transverse piezoelectric beam vibration is developed to address these limitations. Exact expressions for the voltage, current, power, and tip deflection of the piezoelectric beam are derived. Subsequently, several case studies are presented that examine the frequency response of vibration-based energy harvesters using this model. It is shown that the predicted responses converge towards previously derived Euler-Bernoulli beam models under certain limiting conditions. The Timoshenko model shows that the Euler-Bernoulli model severely over-predicts the tip displacement and consequently the power transduction of a cantilevered piezoelectric bimorph at low length-to-width aspect ratios.

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