Influence of restricted operating space on the performance of random vibration energy harvesting

Abstract

The ambition to create self-powered microscale electrical devices motivates scientific and industrial communities to investigate the energy harvesting technique, especially working in random vibration circumstances. The mechanical response of the random vibration system may approach infinity with small probability, and then the restricted operating space of the energy harvesting system will unavoidably induce the occurrence of collision interaction. Here, the random mechanical vibration and electrical output of the vibration energy harvesting system including inelastic collision are investigated, in which the random excitation is described by Gaussian white noise, while the collision interactions are described by the transient impact model and inelastic contact model, respectively. Introducing the generalized harmonic transformation of mechanical states and adopting a slow-varying process assumption of amplitude and averaged frequency, the output voltage can be explicitly expressed as the function of displacement, velocity, and system total energy by directly integrating the linear electrical equation. The transient impact interaction is equivalent to an effective damping with energy-dependent damping coefficient, while the inelastic contact interaction is equivalent to an effective damping and an affiliated potential energy. The averaged equations with respect to mechanical energy are then derived through the stochastic averaging technique. The stationary probabilistic density function of mechanical states is established by solving the reduced Fokker–Plank–Kolmogorov equation, and then the statistical quantities of electrical voltage are obtained by the relation between voltage and mechanical states. The effectiveness and precision of the analytical procedure are validated through the results from Monte Carlo simulations, and the influence of collision interaction on the performance of energy harvesting is discussed in detail. Also, for the energy harvesting system excited by colored noise, the influence of collision interaction on the performance is evaluated through Monte Carlo simulations.