Instability and Nonlinear Dynamic Analyses of Convex Bimorph DE Actuator for Soft Fish Robotic Tail

Abstract

Biomimetic robots are currently experiencing a surge in demand due to their exceptional engineering applications and impressive performance capabilities. The soft fish robot is a novel type of aquatic organism that is constructed using electro-active polymer (EAP) based dielectric elastomer (DE) materials. This unique robot is designed specifically for the purpose of underwater exploration. This type of intelligent/smart actuator can support human interactions or communications with the dynamic environments. These actuators are capable of producing large strains/ mechanical actuation when electric fields are applied. Electrical energy gets converted to mechanical energy during bending actuation of bimorph DE actuator. The present work proposes an anisotropic convex bimorph DE actuator (DEA) to generate the flapping motion in the tail of soft fish robot. The fibers attached in the anisotropic case are oriented in some angles, the convex structure has led to the concept of taper ratio and temperature variation analysis for practical applications is necessary. Therefore, in this present analysis, the fibre angles of the reinforcement, the taper ratios, and the temperatures are varied to study the performance of the system. The instability and nonlinear dynamic responses of the proposed actuator have been studied and analysed by developing the mathematical models. The system is modelled under coupled electro-thermo-mechanical field considering without and with reinforcement of soft fibers in DE layer of such actuator. The equilibrium equations to study the instability have been derived in terms of taper ratios of the convex shaped actuator and the ply angles due to anisotropy at different temperatures. After obtaining the mathematical derivations, numerical solutions of the complex nonlinear equations for critical stretch, nominal electric field, and entropy under different mechanical, electrical, and thermal loads are determined using MATLAB. The observations demonstrated that with growth in nominal stress as well as temperature the peak point of nominal electric field gets enhanced. Results also inferred that with rise in temperature, nominal stress and axial stretch, entropy surges, making the system disordered. After obtaining the range of stability, the dynamic performances of system are studied and analysed. Nonlinear dynamic analyses of the anisotropic convex bimorph DEA are performed to determine bending actuation/flap. Experimentally stress relaxation behaviours of the elastomer at different temperatures are obtained using dynamic mechanical analysis (DMA 8000) to obtain shear moduli (relaxed and unrelaxed) and relaxation time. The thermo-electro-visco-hyperelastic behaviour of such actuators is represented by Gent model of hyperelasticity in conjunction with the new relaxation model of viscoelasticity based on the obtained experimental data. The governing equations of motion are derived based on the Euler Lagrangian principle and solved using MATLAB and Simulink to analyse the nonlinear dynamics of active layer for such actuator. Based on the obtained axial stretch of the active layer, flapping movements of the bimorph DEA have been determined. The effects of the parameters are observed on the time series and frequency responses. The frequency spectrum indicates 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 obtained to represent the physical behaviour of nonlinear dynamics. Then from the responses, it is inferred that with a hike in temperature and taper ratio, the stretch and deflection increase. 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, it is observed that subharmonic, harmonic and super harmonic exists in the system’s responses. At low frequency it is found that the stretch histories are chaotic. It is also identified that in isotropic actuator, the stretch obtained is more compared to anisotropic actuator. The proposed work aims to provide guidance for conducting stability and dynamic performance analyses of bimorph actuators, with the ultimate goal of enabling their integration into high performance underwater robots.