Nonlinear dynamic analysis of anisotropic bimorph dielectric elastomer actuator for soft fish robots

Abstract

Electric fields when applied to smart materials like dielectric elastomers (useful for biomimetic creatures), provide a greater amount of mechanical actuation, but concerns with various drawbacks of isotropic dielectric elastomers whereas by imparting anisotropy through reinforcing soft fibers in such materials is used to overcome the drawbacks associated with it. Thus, in this study, nonlinear dynamic analysis of anisotropic visco-hyperelastic convex tapered bimorph dielectric elastomer actuator is reported to mimic actual fish tail by providing flaps through actuation. Experimental stress relaxations of the elastomer at different temperatures are performed using dynamic mechanical analysis (DMA 8000) to determine shear moduli (relaxed and unrelaxed) and relaxation time. The thermo-electro-visco-hyperelastic behavior of such actuators is represented by the Gent model of hyperelasticity in conjunction with the new relaxation model of viscoelasticity based on the obtained experimental data. Thereby, the governing equation of motion is derived based on Euler Lagrangian principle and solved through MATLAB and Simulink to analyze the nonlinear dynamics of active layer for such anisotropic actuators. For this present analysis, the fiber angles of the reinforcement, the taper ratio, and the temperatures are altered to study the effects of these parameters on the time series and frequency responses. The frequency spectrum shows generation of different frequencies which are linear combination of natural and excitation frequencies. The stretch histories, deflections, phase planes, Poincaré maps along with hysteresis loops and bifurcation diagram are attained to represent the physical behavior of nonlinear dynamics. Then from the responses it is inferred that with an increase in temperature and taper ratio, the stretch and deflection also increases, since the natural frequency and stiffness decreases for particular fiber angle. From the phase portraits, the quasi-periodic nature of the system is evident at dominant spike and the hysteresis loop indicates energy dissipation. From the bifurcation diagram analysis, sub or super of the dominant amplitude of frequency exists. At low frequency it is found that the stretch histories are chaotic.