This paper aims to investigate the chaotic and nonlinear resonant behaviors of a dielectric elastomer-based microbeam resonator, incorporating material and geometric nonlinearities. The von Kármán strain-displacement equation is utilized to model the geometric nonlinearity. Material nonlinearity is described via the hyperelastic Gent model and Neo-Hookean constitutive law. The applied electrical loading to the elastomer includes both static and sinusoidal voltages. The governing equations of motion are formulated based on an energy approach and generalized Hamilton’s principle. Employing a single-mode Galerkin technique, the governing equations are obtained only in terms of time derivatives. The governing ordinary differential equations are solved by means of the multiple scale method and a time-integration-based solver. The nonlinear resonance characteristics are explored through the frequency-amplitude plots. The nonlinear oscillations of the system are analyzed making use of visual techniques such as phase plane diagram, Poincaré section and time history, and fast Fourier transform. Based on the results obtained, the resonant behavior is the hardening type. The vibration of the dielectric elastomer based-microbeam is the quasiperiodic response.

本文旨在研究基于介电弹性体的微梁谐振器的混沌和非线性谐振行为，结合材料和几何非线性。von Kármán 应变-位移方程用于对几何非线性进行建模。材料非线性通过超弹性根特模型和新胡克本构定律进行描述。施加到弹性体的电负载包括静态和正弦电压。运动控制方程是基于能量方法和广义哈密顿原理制定的。采用单模伽辽金技术，控制方程仅根据时间导数获得。控制常微分方程通过多尺度方法和基于时间积分的求解器求解。通过频率-幅度图探索非线性谐振特性。利用相平面图、庞加莱截面和时程以及快速傅立叶变换等视觉技术分析了系统的非线性振荡。根据获得的结果，共振行为是硬化类型。基于介电弹性体的微梁的振动是准周期响应。