Stochastic dynamics of a bistable vibration energy harvesting system with bilateral barriers

The motion of a bis-table energy harvesting system often becomes trapped within a single potential well, leading to a reduction in energy harvesting efficiency. To address this issue, this paper presents a nonlinear energy harvester that integrates an impact mechanism with two symmetrical stops into a bis-table configuration. Based on the equilibrium points of the bis-table vibration energy harvester (BVEH), a specific transformation and stochastic averaging technique are adopted to investigate stochastic response and reliability of this system. This transformation enables the derivation of the averaged Itô stochastic differential equations, from which the stationary probability density function of the system state can subsequently be obtained. The effects of key system parameters on the variation trends of the mean square voltage and mean output power were also investigated. Finally, the backward Kolmogorov (BK) equation governing the conditional reliability function is analytically derived. The effects of system parameters on conditional reliability function and mean first passage time are discussed. Furthermore, the validity of the proposed reliability method is assessed by analyzing relative errors under different parameter configurations. The theoretical results are verified through comparison with Monte Carlo simulations (MCS).