Stochastic analysis of asymmetric monostable harvesters driven by Gaussian white noise with moment differential equations

Abstract

As an effective means to overcome the shortcomings of linear systems only performing well near the resonance frequency, monostable piezoelectric energy harvesters (MPEHs) have been investigated widely in the area of energy harvesting. However, it is difficult to achieve a perfectly symmetric potential energy function due to the asymmetries in magnets and materials. Therefore, the response characteristics of the asymmetric MPEHs with quartic potential function under Gaussian white noise excitation are explored in this paper. The method of moment differential equation is applied to approximately determine the output performance of the asymmetric potential MPEHs under the excitation of Gaussian white noise. For the symmetric MPEH, the influence of external excitation intensity and internal system parameters on the outputs is firstly analyzed theoretically and numerically. When a quadratic nonlinear coefficient is introduced and only using its variation to characterize the variation of the asymmetry, the output performance of the MPEH is enhanced and the power increases with an increase in the asymmetry. Particularly, the existence of asymmetry leads the system to have a nonzero mean value for the displacement response, which then influences the shape of the probability density function. In the condition that more coefficients are employed to represent the asymmetry, the influence of asymmetry on the output depends on the potential energy function’s shape.