Theoretical analysis of piezoelectric energy harvesting system with impact under random excitation

A kind of mono-stable piezoelectric energy harvesting system with unilateral offset barrier under Gaussian white noise excitation is studied theoretically to reveal the physical mechanism in this paper. After utilizing the Zhuravlev transformation and the stochastic averaging method, stationary joint and marginal probability density functions of the displacement and velocity are obtained, as well as the equation of the mean square voltage. Stochastic response characteristics are discussed by analyzing the functions deducted previously. And the effectiveness of the theoretically approximate methods is validated by Monte Carlo simulation results. In addition, effects of the noise intensity, the restitution coefficient, the mechanical damping exponent, and the ratio coefficient between the mechanical and electrical time constant in the system on the mean square voltage are explored.