中文摘要：

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．

英文摘要：

Recently, active soft materials have attracted widespread attention in the flexible device manufacturing industry. As a typical active soft material, the dielectric elastomer, with two compliant e- lectrodes covering its upper and lower surfaces, constitutes the dielectric elastomer structure. Although the dielectric elastomer structure possesses excellent electromeehanical properties, various failures occur frequently when operating in the dynamic environment, which greatly hinders its extensive application. The dynamic stability of an ideal spherical dielectric elastomer balloon is investigated here, which is related to the phenomenon of electro-mechanical instability. Firstly, the governing differential equation with re- spect to the stretch ratio of the ideal spherical dielectric elastomer balloon is derived according to the princi- ple of virtual work. The free energy function is expressed as the summation of the dielectric energy and the elastic energy described by the Mooney-Rivlin model. Secondly, the relation between the peak value of sta tionary response and the step voltage/pressure is analytically derived through the first integral of system. The intersection point of the relation curve and the static equilibrium curve gives the critical voltage/pres- sure. The instability of the spherical dielectric elastomer balloon under different situations is discussed in detail. For any given voltage, there exists a threshold of material constant, below which the structure will remain stable forever. A similar threshold of material constant exists for any pressure with the value of nonzero. For the case with absent pressure, however, there exists a critical voltage, beyond which the structure will be dynamically instable. The influences of the imposed voltage/ pressure, material constant and pre-stretch on the critical state of the dynamic instability are investigated systematically. Pre-stretch will improve the dynamic stability of the spherical dielectric elastomer balloon. This work paves the way for the theo