This paper delves into the analysis of nonlinear deformation induced by dielectric actuation in pre-stressed ideal dielectric elastomers. It formulates a nonlinear ordinary differential equation governing this deformation based on the hyperelastic model under dielectric stress. Through numerical integration and neural network approximations, the relationship between voltage and stretch is established. Neural networks are employed to approximate solutions for voltage-to-stretch and stretch-to-voltage transformations obtained via an explicit Runge-Kutta method. The effectiveness of these approximations is demonstrated by leveraging them for compensating nonlinearity through the waveshaping of the input signal. The comparative analysis highlights the superior accuracy of the approximated solutions over baseline methods, resulting in minimized harmonic distortions when utilizing dielectric elastomers as acoustic actuators. This study underscores the efficacy of the proposed approach in mitigating nonlinearities and enhancing the performance of dielectric elastomers in acoustic actuation applications.

翻译：本文深入分析了预拉伸理想介电弹性体在介电驱动下产生的非线性变形。基于介电应力下的超弹性模型，推导了描述该变形的非线性常微分方程。通过数值积分与神经网络逼近，建立了电压与拉伸比之间的函数关系。采用神经网络对显式龙格-库塔法求解得到的电压-拉伸比及拉伸比-电压变换进行逼近，并利用这些逼近结果对输入信号进行波形整形以实现非线性补偿，从而验证了其有效性。对比分析表明，与基准方法相比，逼近解具有更高的精度，在使用介电弹性体作为声学驱动器时可将谐波失真降至最低。本研究凸显了所提方法在抑制非线性及提升介电弹性体声学驱动性能方面的有效性。