气压扰动下介电弹性体球膜的随机响应分析

研究随机扰动的压力和恒常电压联合作用下的介电弹性体球膜,发展随机响应的分析方法并总结其规律,为计及介电弹性体的应变强化现象,其力学性能由Gent应变能模型描述,压力扰动近似为高斯白噪声.引入能量相关变换并应用随机平均法导出了关于系统总能量稳态概率密度的简化Fokker-Planck-Kolmogorov方程,并解析得到方程的解,从而得到球膜伸长比及其变化率的稳态概率密度,进而得到伸长比的各阶统计量.研究针对两种典型情形进行,即球膜在伸长比为1附近的振动及球膜在材料拉伸极限附近的振动.详细讨论了激励强度、材料参数及常电压值对伸长比统计量的影响,特别强调了不同的材料参数和常电压值引起的不同振动模式.蒙特卡洛模拟证实了分析结果的有效性和精度.

Random response of dielectric elastomer balloon subjected to disturbed pressure

The random response of dielectric elastomer balloon subjected to random pressure and constant voltage is investigated, where the mechanical property is described by Gent model in order to consider the strain stiffening effect of the dielectric elastomer, and the random pressure is described by Gaussian white noise. By introducing the energy dependent transformation and using the stochastic averaging, the reduced Fokker Planck Kolmogorov equation governing the stationary probability density of the system total energy is derived, which can be analytically solved. The marginal probability densities of the stretch ratio and its change ratio are then calculated, as well as the mean value and the mean square value of the stretch ratio. Two typical cases are investigated in detail, i.e., one is with the stretch ratio of balloon vibrating of around 1 and the other is that around the extension limit. The influences of the random excitation intensity, material parameter and the constant voltage on the statistics of the stretch ratio are discussed in detail. Different values of the material parameter and the constant voltage can cause completely different random vibration behaviors. The efficacy and accuracy of the proposed procedure are eventually verified by comparing with the results from Monte Carlo simulation.