Response analysis of the piezoelectric energy harvester under correlated white noise

Energy harvesting of a monostable duffing-type harvester with piezoelectric coupling under correlated multiplicative and additive white noise is investigated in this paper. The generalized harmonic transformation is applied to decouple the electromechanical equations, which leads to an uncoupled equivalent nonlinear system. Using the stochastic averaging method, an analytical solution of random response for vibration energy harvesters (VEHs) is obtained. The effects of the system parameters on the mean-square displacement, the mean output power and the power spectral density are explored. It is found that the correlated noise can improve the performance of the nonlinear VEHs. The curve of the mean output power first increases with increasing the ratio of time constant, reaches a maximum and then decreases. This phenomenon is of great significance to energy harvesting. Finally, the theoretical results are well verified through the numerical simulations.