A Timoshenko beam model for cantilevered piezoelectric energy harvesters

Abstract

Piezoelectric bimorph cantilevered beams are often used as energy harvesting devices.These devices are desired for, among other applications, remote sensing and animaltracking due to their potential for eliminating the need for battery replacement. Existingmodels of piezoelectric bimorph cantilevered beams have proved to describe the dynamicsof slender beams at high frequencies accurately. In this paper, a Timoshenko model oftransverse piezoelectric beam vibration is developed to address these limitations. Exactexpressions for the voltage, current, power, and tip deflection of the piezoelectric beam arederived. Subsequently, several case studies are presented that examine the frequencyresponse of vibration-based energy harvesters using this model. It is shown that thepredicted responses converge towards previously derived Euler–Bernoulli beam modelsunder certain limiting conditions. The Timoshenko model shows that the Euler–Bernoullimodel severely over-predicts the tip displacement and consequently the powertransduction of a cantilevered piezoelectric bimorph at low length-to-width aspect ratios.