Stochastic response of bistable vibration energy harvesting system subject to filtered Gaussian white noise

Mechanical vibrations have been proved to be a clean and reliable energy source, especially the bistable model can enhance the efficiency of vibration energy harvesting under the case of low-level vibration and attracts more and more attention. In this manuscript, an improved coordinate transformation, based on the equilibrium points of bistable vibration energy harvesting (BVEH) system, is proposed to construct a quasi-conservative stochastic averaging procedure, and this method is applied to the nonlinear BVEH system driven by filtered Gaussian white noise to obtain the dynamic behaviors. Through this transformation, the nonlinear electromechanical coupling BVEH system can be approximated by an equivalent single degree of freedom bistable system, which contains the energy-dependent frequency functions and the equilibrium points. The analytic expressions of the stationary probability density function of the system state can be obtained by the quasi-conservative stochastic averaging method, and by applying the relationship between the output voltage and the state variables of the system, the mean-square output voltage (MSOV) and the mean output power (MOP) will be obtained. Finally, the variation trends of MSOV and MOP depended on the physical quantities of stochastic BVEH system, such as the excitation intensity and the peak frequency of seismic motion of the filtered Gaussian white noise, the parameters of the vibration system and the electromechanical coupling coefficients, are also analyzed in detail. Corresponding theoretical results are well verified through the direct Monte Carlo simulation.