Abstract Dielectric elastomer minimum energy structure (DEMES) formed by clinging a pre-stretched dielectric elastomer (DE) membrane to the compliant frame possess both material and geometrical nonlinearity. The viscous and hyperelastic nature of the DE membrane and coupling between the compliant frame and membrane forms the basis of these nonlinearities. Practically, DE membrane based DEMES actuator executes the transient motion which is significantly affected by the viscoelastic behavior of the DE membrane. Hence, for an efficient design of such devices, it is very important to analyse the effect of membrane viscoelasticity on the dynamic response of DEMES. In the present work, we have developed an analytical model to analyse the viscoelastic effect of DE membrane on the nonlinear dynamic behavior of the DEMES. In order to incorporate the viscous effect, the Zener rheological model consisting of a spring element connected in parallel to a Maxwell element is employed. The neo-Hookean material model based on the additive decomposition of the isotropic strain energy density into equilibrium and viscous parts is considered. The governing differential equation representing the dynamic behavior of DEMES actuator is derived using Euler–Lagrange equation of motion for non-conservative system. The isotropic viscous stretch is obtained by using the thermodynamically consistent evolution equation. The developed dynamic model predicts the initial shape, DC and AC response, periodicity of the DEMES for different values of viscosity parameter. The result reveals that the onset of equilibrium state delays as viscosity parameter increases. Further, the bending angle of DEMES actuator is significantly affected by the applied electric field and viscoelastic behavior of the DE membrane. Poincare maps along with phase diagrams are presented to analyse the periodicity of nonlinear oscillation of the system. Further, the structure executes a stability transition (stable-unstable-stable) as the value of viscosity parameter increases. The obtained results can help in robust and efficient designing of DEMES based actuators subjected to dynamic loading.

中文翻译：

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粘弹性对介电弹性体最小能量结构非线性动力学行为的影响

摘要 通过将预拉伸的介电弹性体 (DE) 膜粘附到柔顺框架上形成的介电弹性体最小能量结构 (DEMES) 具有材料和几何非线性。DE 膜的粘性和超弹性性质以及柔顺框架和膜之间的耦合构成了这些非线性的基础。实际上，基于 DE 膜的 DEMES 执行器执行瞬态运动，该运动受到 DE 膜的粘弹性行为的显着影响。因此，对于此类装置的有效设计，分析膜粘弹性对 DEMES 动态响应的影响非常重要。在目前的工作中，我们开发了一个分析模型来分析 DE 膜对 DEMES 非线性动态行为的粘弹性影响。为了结合粘性效应，采用由并联连接到麦克斯韦元件的弹簧元件组成的齐纳流变模型。考虑了基于将各向同性应变能量密度加性分解为平衡部分和粘性部分的新胡克材料模型。使用非保守系统的欧拉-拉格朗日运动方程推导出代表 DEMES 执行器动态行为的控制微分方程。各向同性粘性拉伸是通过使用热力学一致演化方程获得的。开发的动态模型预测初始形状、直流和交流响应、不同粘度参数值的 DEMES 的周期性。结果表明，平衡状态的开始随着粘度参数的增加而延迟。更多，DEMES 致动器的弯曲角度受外加电场和 DE 膜的粘弹性行为的显着影响。提出了庞加莱图和相图来分析系统非线性振荡的周期性。此外，随着粘度参数值的增加，该结构执行稳定性转变（stable-unstable-stable）。获得的结果有助于在动态载荷下基于 DEMES 的执行器的鲁棒性和高效设计。随着粘度参数值的增加，该结构执行稳定性转变（稳定-不稳定-稳定）。获得的结果有助于在动态载荷下基于 DEMES 的执行器的鲁棒性和高效设计。随着粘度参数值的增加，该结构执行稳定性转变（稳定-不稳定-稳定）。获得的结果有助于在动态负载下基于 DEMES 的执行器的鲁棒性和高效设计。