]Dielectric elastomer(DE)is a polymer material with flexible electrodes that exhibit significant electromechanical response when subjected to an electric field.It is widely used in various fields like materials manufacturing,aerospace,bionic machinery,and biomedical engineering because of its fast response,large strain,high conversion efficiency,and affordability.In consideration of the preci-sion requirements and the difficulty in ensuring constant radial force,this paper first introduces Gauss-ian white noise as a random small disturbance to simulate radial force.A stochastic dynamic model with fractional-order damping is developed under the coupling effect of random radial force and DC voltage.Then,the steady-state probability density functions of stretch ratio and stretch ratio velocity are solved using the stochastic averaging method based on the generalized harmonic function.Mean while,the re-sponse is validated through Monte Carlo simulations.Finally,the influence of electromechanical cou-pling parameters on the system's mono-stable and bi-stable states is investigated.Furthermore,the ef-fects of noise intensity and fractional order on the dynamic response of DE are analyzed in detail from the perspective of two stable states.
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