Asymptotic stability of a nonlinear energy harvester with mass disturbance undergoing Markovian jump

Stochastic mass has exerted a profound impact on the dynamics of the systems characterized by light mass and compact volume. This work delves into the asymptotic stability with probability one of a variable mass energy harvester. Firstly, the Gaussian white noise with Markovian jump is coupled to model the inherent randomness and discreteness of stochastic mass. Then, we have established an approximate dimensionless system based on an equivalent transformation. Using the stochastic averaging method, the averaged Itô stochastic differential equation of the amplitude within the approximated system is derived. With the linearization, we have deduced the largest Lyapunov exponent for the linearized equation. Furthermore, the necessary and sufficient condition for achieving asymptotic stability of the nonlinear energy harvester is proposed approximately by managing the largest Lyapunov exponent be negative. The study systematically dissects the effects of stochastic mass and Markovian jump on the asymptotic stability with probability one of a nonlinear energy harvester. Under the disturbance of stochastic mass, with the increase of linear stiffness, the stability of the system will change nonlinearly. Moreover, the stability regions of the nonlinear energy harvester under varying transition matrices and stochastic mass noise intensities are thoroughly given. The findings and conclusions presented in this paper have a certain theoretical significance for the management of the system stability in engineering practical.