Nonlinear nonconservative behavior and modeling of piezoelectric energy harvesters including proof mass effects

Abstract

Nonlinear piezoelectric effects in flexural energy harvesters have recently been demonstrated for drive amplitudes well within the scope of anticipated vibration environments for power generation. In addition to strong softening effects, steady-state oscillations are highly damped as well. Nonlinear fluid damping was previously employed to successfully model drive dependent decreases in frequency response due to the high-velocity oscillations, but this article instead harmonizes with a body of literature concerning weakly excited piezoelectric actuators by modeling nonlinear damping with nonconservative piezoelectric constitutive relations. Thus, material damping is presumed dominant over losses due to fluid-structure interactions. Cantilevers consisted of lead zirconate titanate (PZT)-5A and PZT-5H are studied, and the addition of successively larger proof masses is shown to precipitate nonlinear resonances at much lower base excitation thresholds while increasing the influence of higher-order nonlinearities. Parameter identification results using a multiple scales perturbation solution suggest that empirical trends are primarily due to higher-order elastic and dissipation nonlinearities and that modeling linear electromechanical coupling is sufficient. This article concludes with the guidelines for which utilization of a nonlinear model is preferred.