Resonance mechanism of nonlinear vibrational multistable energy harvesters under narrow-band stochastic parametric excitations

To improve energy harvesting performance, this paper investigates the resonance mechanism of nonlinear vibrational multistable energy harvesters under narrow-band stochastic parametric excitations. Based on the method of multiple scales, the largest Lyapunov exponent which determines the stability of the trivial steady-state solutions is derived. The first kind modified Bessel function is utilized to derive the solutions of the responses of multistable energy harvesters. Then, the first-order and second-order nontrivial steady-state moments of multistable energy harvesters are considered. To explore the stochastic bifurcation phenomenon between the nontrivial and trivial steady-state solutions, the Fokker-Planck-Kolmogorov equation corresponding to the two-dimensional Itô stochastic differential equations is solved by using the finite difference method. In addition, the mechanism of the stochastic bifurcation of multistable energy harvesters is analyzed for revealing their unique dynamic response characteristics.