Nonlinear dynamics of dielectric actuator: Exploring electrode mechanics

Dielectric elastomer (DE) is a smart material with various biomedical, soft robotics, and vibration control applications. Modeling of the DE actuator is essential for its practical applicability by virtue of its nonlinear characteristic. Many existing models neglect the effect of the electrode despite substantial experimental work demonstrating the electrode’s influence. This work presents the model and nonlinear analysis of the equi-biaxial motion of a planar dielectric membrane incorporating the effect of the electrode. The uniqueness of the paper is due to the inclusion of terms related to inertia, stiffness and damping of the electrode in the governing equation. The elastomer and the electrode are both assumed to be hyperelastic materials having different physical properties, and the governing equation is derived by considering the mechanical aspects of both the elastomer and electrode materials. The behavior of the system for both constant and time-varying voltages is analyzed. Static response and its dependence are explored by presenting the equilibrium stretch plot, potential energy characteristics, and the basin of attraction. The analysis is further expanded for the time-varying voltage, and the impact of the electrode material on the system’s stretch range is also demonstrated. Backward and forward frequency sweeps are used to obtain the amplitude–frequency response and show its dependence on the electrode. Furthermore, time response, phase plot, Poincare map, and Lyapunov exponent are utilized to demonstrate the impact of the mechanical characteristic of the elastomer and electrode on the overall dynamics. The proposed model is validated with the experiment for different voltage conditions. A comparison is also presented between the experiment and system behavior with and without the electrode effect. The findings indicate that the electrode influences the static and dynamic response of the actuator. This work gives a more realistic model of the DE actuator and guides more accurate design of the actuator for various applications.