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介电弹性体结构具有卓越的力电性能,然而由于其大变形特性,在动态工作模式下极易出现各类失效问题,这极大阻碍了其工程应用.论文研究与力电失稳行为直接相关的理想介电弹性球膜动力稳定性问题.首先据虚功原理建立电压及压力共同作用下关于伸长比的动力学方程,系统自由能由弹性应变能与静电能组成,而前者基于Mooney-Rivlin模型表出.通过系统首次积分解析给出稳态响应峰值与阶跃电压/阶跃压力的关系曲线,其与静态平衡曲线的交点决定了临界电压/临界压力.研究表明:给定任意电压,材料参数存在某阈值,当超过该值后系统始终保持稳定;对于任意非零压力值,存在类似材料参数阈值;而当压力恰为零时,则始终存在临界电压值,超过该值则系统动力不稳定.
However, due to its large deformation characteristics, it is very easy to find all kinds of failure problems under dynamic working mode, which has greatly hindered its engineering application.The thesis studies the direct failure of force-electricity instability Related to the dynamic stability of the ideal dielectric elastic spherical membrane.Firstly, based on the principle of virtual work, the dynamic equations of elongation under voltage and pressure are established. The system free energy consists of elastic strain energy and electrostatic energy. The former is based on Mooney -Rivlin model.The first time integral analysis shows the steady-state response peak and step voltage / step pressure curve, the intersection with the static equilibrium curve determines the critical voltage / critical pressure.The results show that: given arbitrary There is a threshold for voltage and material parameters, and the system remains stable when it exceeds this value. Similar material parameter thresholds exist for any non-zero pressure value, and when the pressure is exactly zero, there is always a threshold voltage value beyond which System power instability.