Probability and output analysis of asymmetric bistable energy harvesters subjected to Gaussian white noise

Due to their excellent broadband response and high sensitivity to low-amplitude excitations, there is significant interest in the theoretical analysis and experimental validation of bistable energy harvesters (BEHs). However, it is difficult in practice to obtain a perfectly symmetric bistable potential energy function, and our current understanding of the influence of asymmetric potentials on the response of BEHs is limited. As a result, this paper sheds light on the influence of asymmetric potentials on the response probability and electrical outputs of BEHs driven by Gaussian white noise. Firstly, the influence of potential well depth on the power outputs and response probability of symmetric BEHs is illustrated. When a quadratic nonlinearity is introduced to characterize the asymmetry, numerical simulations demonstrate that it has a negative effect on the output of BEHs when the noise intensity is relatively low, and the negative influence becomes great with an increase in the degree of asymmetry. From the probability analysis, it is concluded that the probability density function of displacement strongly depends on the degree of asymmetry of the potential function and it is also affected by the excitation intensity. Finally, experiments are carried out which demonstrate that the average output power is indeed influenced by the asymmetric potential of the BEHs under different excitation levels.