Assumed-modes modeling of piezoelectric energy harvesters: Euler–Bernoulli, Rayleigh, and Timoshenko models with axial deformations

A generalized framework is presented for the electromechanical modeling of base-excited piezoelectric energy harvesters with symmetric and unsymmetric 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 and its electromechanical coupling in all cases. Comparisons are provided against the analytical solution for symmetric laminates and convergence of the assumed-modes solution to the analytical solution with increasing number of modes is shown. Model validations are also presented by comparing the electromechanical frequency response functions derived herein with the experimentally obtained ones in the absence and presence of a tip mass attachment. A discussion is provided for combination of the assumed-modes solution with nonlinear energy harvesting and storage circuitry. The electromechanical assumed-modes formulations can be used for modeling of piezoelectric energy harvesters with moderate thickness as well as those with unsymmetric laminates and varying geometry in the axial direction.