Stochastic averaging for bistable vibration energy harvesting system

Abstract

Vibration energy harvesting technique provides the possibility of the development of self-sustaining microelectronic components. The bistable energy harvesting devices have higher efficiency than the traditional mono-stable devices and deserve further investigation. In this manuscript, a novel stochastic averaging procedure is established to evaluate the stationary random response of bistable energy harvester to additive and multiplicative white noises. An equivalent nonlinear system associated with the original coupling system is first derived by integrating the circuit equation and adopting the assumption of generalized harmonic functions of sample responses. The stationary probability density for mechanical energy of the equivalent nonlinear system is then derived through the stochastic averaging technique. The mean-square mechanical responses, the mean-square voltage and the mean output power are obtained analytically. Finally, the influences of crucial parameters, such as excitation intensity, coupling factor, time constant ratio etc., on mean-square voltage and mean output power are discussed in detail which may provide some guidance for structural design for maximizing output power.