Stochastic and deterministic responses of an asymmetric quad-stable energy harvester

In this paper, stochastic and deterministic dynamical properties of an asymmetric quad-stable energy harvester are explored for improving the energy harvesting performance. Firstly, the harmonic balance method is utilized to explicitly derive the coupled relationship of the displacement amplitude, the constant term, and the output voltage amplitude. By means of direct numerical results, the existence of the multi-valued phenomenon of the asymmetric quad-stable energy harvester is found. Especially, the constant term is asymmetric due to the asymmetric characteristics. In addition, the influence of the depth of different potential wells on the highest orbit of inter-well oscillations is discussed. Finally, it is found that the symbol change of the largest Lyapunov exponent (LLE) of the harvester is consistent with the results derived by bifurcation diagrams, which verify the effectiveness of the LLE. The existence of noise can induce the harvester to transform from period motions to chaotic motions. The transition of the probability density function (PDF) of the harvester is influenced by the potential distribution and depth.