A Timoshenko beam model for cantilevered piezoelectric energy harvesters

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.