In this paper, nonlinear resonance characteristics of a dielectric elastomer actuator are investigated with special consideration on the thermal effects. A finite thermo-elasticity model based on the Gent model is constructed to analyze the vibrational response of the system. The equation of motion is derived via the Euler–Lagrange method. The multiple scales method and the Taylor series expansion are used to solve the governing equation. Nonlinear resonant responses of the system such softening/hardening and jump are explored. Furthermore, the influences of different system parameters including temperature, limiting stretch, damping, mechanical load, relative permittivity and voltage on the frequency response curves are explored. The results are compared with those obtained in the isothermal state, and those solved by numerical methods. It is found that both softening and hardening-type nonlinearities occur in the system in both non-thermal and thermal conditions.

中文翻译：

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介电弹性体致动器在热和等温条件下的非线性共振分析

本文研究了介电弹性体致动器的非线性共振特性，并特别考虑了热效应。构建了基于Gent模型的有限热弹性模型来分析系统的振动响应。运动方程是通过欧拉-拉格朗日方法推导出来的。多尺度方法和泰勒级数展开用于求解控制方程。探索了系统的非线性共振响应，例如软化/硬化和跳跃。此外，还探讨了不同系统参数（包括温度、极限拉伸、阻尼、机械负载、相对介电常数和电压）对频率响应曲线的影响。结果与在等温状态下获得的结果以及通过数值方法求解的结果进行了比较。