An equivalent spring-based model to couple the motion of visco-hyperelastic dielectric elastomer with the confined compressible fluid/air mass

Soft materials exhibiting large voltage-induced deformation under external stimuli have gained increasing attention in the recent past owing to their potential applications in soft transducers. Dielectric elastomer actuators (DEAs) coupled with a fluid/air mass have proved to undergo considerable voltage-induced deformation. This article presents a framework to couple the motion of an inflated Dielectric elastomer (DE) membrane with a confined compressible fluid/air mass and develops a nonlinear dynamic analytical model to predict the polar region deflection of an inflated DE membrane attached to an airtight chamber (namely bulging actuators) stimulated by an electric field. In order to derive the differential equations which determine the dynamic behavior of the membrane coupled to an airtight chamber, the Euler–Lagrange equation is employed, which takes into account the effects of membrane pre-stretch, initial inflation pressure, membrane viscoelastic behavior, and transient electric loading. A hypothesis of pseudo-air-spring is incorporated to consider the effect of the volume of the confined fluid/air mass. The experimental investigation conducted for various geometrical and loading conditions in both depressurized and pressurized states of actuation shows that the developed nonlinear model satisfactorily predicts the influence of fluid/air mass on the dynamic response of the considered DE membrane undergoing small voltage-induced deformation. Finally, the proposed framework is incorporated for building insights on several effecting parameters such as inflation pressure, quality, and quantity of the confined fluid mass, etc., on the electrodynamic behavior of the actuator. The results reveal that the volume of the air column appreciably alters the nonlinear dynamic behavior of the bulging actuator. Poincaré plots along with phase diagrams are presented for analyzing the periodicity of the nonlinear oscillations of the actuator. The underlying theoretical framework and the obtained inferences of the present article can be implemented effectively in the design of a futuristic class of structures whose motion is coupled with compressible fluid/ air mass subjected to time-dependent actuation.