Assumed-Modes Formulation of Piezoelectric Energy Harvesters: Euler-Bernoulli, Rayleigh and Timoshenko Models With Axial Deformations

Abstract

Harvesting of vibration energy has been investigated by numerous researchers over the last decade. The research motivation in this field is due to the reduced power requirement of small electronic components such as wireless sensor networks used in monitoring applications. The ultimate goal is to power such devices by using the waste vibration energy available in their environment so that the maintenance requirement for battery replacement is minimized. Among the basic transduction mechanisms that can be used for vibration-to-electricity conversion, piezoelectric transduction has received the most attention due to the large power densities and ease of application of piezoelectric materials. Typically, a piezoelectric energy harvester is a cantilevered beam with one or two piezoceramic layers and the source of excitation is the base motion in the transverse direction. This paper presents general formulations for electromechanical modeling of base-excited piezoelectric energy harvesters with symmetric and asymmetric laminates. The electromechanical derivations are given using the assumed-modes method under the Euler-Bernoulli, Rayleigh and Timoshenko beam assumptions in three sections. The formulations account for an independent axial displacement variable in all cases. Comparisons are provided against the analytical solution given by the authors for symmetric laminates and convergence of the assumed-modes solution to the analytical solution with the increasing number of modes is shown. Experimental validations are also presented by comparing the electromechanical frequency response functions derived here against the experimentally obtained ones. The electromechanical assumed-modes formulations given here can be used for modeling of piezoelectric energy harvesters with asymmetric laminates as well as those with moderate thickness and varying geometry in the axial direction.