Statistical quantification of DC power generated by bistable piezoelectric energy harvesters when driven by random excitations

Vibration energy harvesting provides prominent potential on leveraging the converted energy to realize self-powered electronics. To satisfy the demand of electronics and rechargeable batteries for DC voltages in practical applications, the high-performing, nonlinear bistable energy harvesters are considered to be interfaced with standard rectifying electrical circuits to extract DC power from environment-like, random base accelerations. To lead to an effective and efficient set of design guidelines for system development, this research proposes a theoretical method to characterize the stationary stochastic dynamic responses and the energy harvesting performance under white noise accelerations. Considering that the bistable harvesters possess multiple vibration regimes which induce drastically different energy harvesting performances, a novel state-probability estimation approach is presented based on the theoretically predicted probability density function (PDF) of system energy to statistically classify the stationary probability of the stochastic vibrations being in the snap-through or intrawell states. Via investigating the effects of the base acceleration strength and system parameters on the dynamic responses and harvested DC power, it is revealed that high energy harvesting performance would be achieved via low system damping and suitable system parameters, such as moderate coupling constant and load resistance. The theoretical predictions are compared with numerical simulations and experimental results to validate the effectiveness of the proposed theoretical method.