Nonlinear Stochastic Oscillation of a Single-Degree-of-Freedom Dielectric Elastomer Generator

This paper investigates the stochastic nonlinear dynamic response of a single-degree-of-freedom dielectric elastomer generator under the combined action of harmonic excitation and stochastic disturbance. First, the nonlinear vibration model of a single-degree-of-freedom dielectric elastomer generator is established. The average method and fourth-order Runge–Kutta method are used to analyze the influence of pre-stretching, the initial membrane length, the charge amount, and the external excitation amplitude on the system response. Considering stochastic disturbance, the stochastic average method is applied to determine the probability density function (PDF) of the system’s steady-state response, and Monte Carlo numerical simulations are compared with the theoretical calculations for verification. The oscillation amplitude of the steady-state response can be increased by increasing the pre-stretching, harmonic excitation amplitude, and stochastic disturbance intensity. In the case of stochastic disturbance, as the intensity of the disturbance increases, the system becomes more likely to exhibit large amplitude responses for longer durations.