An Improved Stochastic Averaging on the Piezoelectric Vibrational Harvester Model with Stiffness and Inertia Nonlinearities

Abstract

In this paper, an improved stochastic averaging method is introduced to solve a monostable piezoelectric vibration energy harvester (VEH) model subject to basal Gaussian white and colored noises. First, the electric voltage is expressed as perturbations to the linear stiffness term and the damping term of the vibrational equation. Second, the original model is simplified into an Itô differential equation by the improved stochastic averaging method. Third, stationary solution of the Fokker–Plank–Kolmogorov function driven from the Itô equation is obtained, so that the stationary probability density functions (PDFs) of the displacement, velocity, and electrical voltage are obtained. With the help of the Monte Carlo, the effectiveness of these theoretical predictions is verified. Finally, the impacts of the nonlinear stiffness coefficient and nonlinear inertia coefficient on the responses are compared. It is found that the stiffness nonlinearity has stronger effect on the output electric voltage than the inertia nonlinearity.