A viscoelastic energy harvester: probabilistic and bifurcation analysis

The dynamics of energy harvesting system have received explosive attention in the last few years, but investigations are restricted to energy harvesting system without viscoelastic term. The crucial difference of the present study and previous studies is that we consider the viscoelastic property and the random excitation simultaneously. The stochastic P-bifurcation problem of energy harvester with viscoelastic term driven by colored noise is investigated in this article. To successfully achieve this goal, the viscoelastic force can be equivalently converted to quasilinear damping and quasilinear stiffness by the aid of approximate conversion, and then, the original system can be transformed into a nonlinear stochastic system without viscoelasticity. Based on this work, combining the stochastic averaging method and decoupling method, one can obtain the Fokker–Planck–Kolmogorov equation and the stationary probability density function expression of vibration amplitude. The effectiveness of the proposed method is verified by the consistency of Monte Carlo simulations and analytical results. Furthermore, the critical parameter conditions of the stochastic P-bifurcation are discussed by using singularity theory and extreme value principle. Meanwhile, the change of noise intensity, correlation time, and viscoelastic parameters can induce the occurrence of stochastic bifurcation phenomenon. Ultimately, the influences of various parameters on the stationary mean amplitude and mean output power are examined in detail, which has important practical significance for choosing control parameters to enhance the performance of energy harvesting system with viscoelastic term.