一类圆柱形介电弹性体的随机响应分析

Random Response Analysis of a Class of Cylinder-shaped Dielectric Elastomer

介电弹性体(简称DE)是一种具有柔性电极的聚合物材料,当施加电场时,会出现显著的机电响应.由于其响应速度快、应变大、机电转化率高且成本低等优点,DE的应用已广泛涉及材料制造、航空航天、仿生机械和生物医学等领域.考虑到许多应用装置对精准度的要求,以及固定不变的径向力难以保证的问题,首先采用高斯白噪声模拟径向力的随机小扰动,建立了在随机径向力和直流电压耦合作用下含有分数阶阻尼的随机动力学模型.进而利用广义谐和函数随机平均法求解了拉伸比率和拉伸比速率的稳态概率密度函数,并通过蒙特卡洛模拟进行验证.最后,研究了机电耦合参数对系统单稳态和双稳态的影响,并从两种稳态角度详细分析了噪声强度和分数阶阶数对DE动力学响应的影响.

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 precision requirements and the difficulty in ensuring constant radial force,this paper first introduces Gaussian 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.Meanwhile,the response is validated through Monte Carlo simulations.Finally,the influence of electromechanical coupling parameters on the system's mono-stable and bi-stable states is investigated.Furthermore,the effects of noise intensity and fractional order on the dynamic response of DE are analyzed in detail from the perspective of two stable states.