Reliability and First-Passage Time of Nonlinear Stochastic Rotational Energy Harvester

This paper studies the first-passage reliability of a two-degree-of-freedom (2-DOF) nonlinear stochastic rotational vibration energy harvester under random excitation. Firstly, a nonlinear dynamical model of the system is developed and reduced to a one-dimensional energy diffusion process via the stochastic averaging method (SAM) for quasi-non-integrable Hamiltonian systems. Secondly, the backward Kolmogorov (BK) equation and the generalized Pontryagin (GP) equation are derived to characterize the first-passage behavior. By imposing appropriate boundary conditions, the conditional reliability function, the conditional probability density function (CPDF), and statistical moments of the first-passage time are obtained by solving the associated BK and GP equations. Finally, the SAM results were compared with Monte Carlo (MC) simulations to verify the effectiveness of the proposed approach. Based on this foundation, a systematic analysis was conducted to evaluate the effects of initial energy, noise intensity, and key dynamic parameters on the conditional reliability function, the CPDF of the first-passage time, and mean first-passage time (MFPT). Results indicate that increasing the generator natural frequency and electromagnetic damping ratio markedly enhances system reliability, whereas mechanical damping and Coulomb friction provide weaker but beneficial effects within the investigated ranges. The initial energy and noise intensity are identified as the dominant factors in the sensitivity analysis, while the cubic-stiffness-related characteristic frequency, mechanical damping, and Coulomb friction play relatively minor roles. The present study provides a reduced diffusion modeling and first-passage analysis framework for nonlinear stochastic dynamical systems, while also offering reliability-oriented insights for rotational vibration energy harvesters.