Response analysis of the archetypal smooth and discontinuous oscillator for vibration energy harvesting

In this paper, the archetypal smooth and discontinuous (SD) oscillator considered the gravity is presented for the electromagnetic vibration energy harvesting driven by stochastic environmental fluctuation. This oscillator is composed of a lumped mass connected with a vertical spring and a pair of horizontally springs, which can achieve the bistability widely used in vibration energy harvesting. Based on the stochastic averaging method, the analytical solutions of random responses are obtained and reveal interesting dynamics related to the stationary and transient properties of the device. Then, the influences of the system parameters on the mean square electric current and the mean output power are explored by an analytical method and validated by numerical simulation. Finally, the modelling of electromagnetic bistable harvester under the simultaneous action of harmonic and stochastic excitations is developed, and the condition for the occurrence of stochastic resonance is defined conventionally by the Kramers rate.