Nonlinear Dynamics of Soft Actuators: Stiffness of Elastomer-Electrode Interactions

Dielectric elastomer (DE) has applications in various fields like biomedical, aerospace, pumps, and tactile display. However, its nonlinear characeristics pose as a barrier for its practical applicability. The mathematical models that have been presented till now have not considered the stiffnessof the electrode, generally. However, the electrode’s stiffness does effect the motion of the DE actuator. The mathematical model and nonlinear dynamics of the dielectric elastomer based actuator considering the electrode stiffness is presented in this work. Along with that, the axial effect of the elastomer is also considered to incorporate the dimension of the elastomer. The model is utilized to provide insights into the influence of the electrode and elatomer's geometry on the response of the elastomer. The constant and time-varying voltages are considered to get the static and dynamic behavior of the system. The potential energy behavior and the corresponding equilibrium states of the system is presented. Further, the impact of initial condition, dimension and damping on the equilibrium state achieved for the double-well potential is also described. The influence of shear modulus on the snap-through instability is also examined in this study. Amplitude frequency response is illustrated and the effect of various parameters on it is also analysed. The dynamic response, whether periodic or chaotic, is described and the influence of parameters on it has also been explored. This research helps selecting membrane systems for specific applications by providing a understanding of the factors that influence actuator performance. The study also highlights the importance of dynamic behavior analysis, including the transition between periodic and chaotic responses, which is crucial for designing actuators that can function reliably under different conditions.