Axisymmetric Vibration of Inviscid Compressible Fluid-Filled Soft Dielectric Elastomer Actuator Tube

Driven by the versatility and adaptability of next-generation soft robotic devices, investigating the vibrational behavior under fluid-electromechanical coupling represented by a soft dielectric elastomer actuator (DEA) tube filled with fluid evokes much attention. Here, we investigate the axisymmetric vibration of an inviscid compressible fluid-filled thin DEA tube by using the Gent model to define the behavior of the tube under multi-fields. We consider the effect of the fluid by exploiting the relation of the radial fluid pressure at the fluid–solid interface. Following the general incremental theory of nonlinear electro-elasticity, we formulate the incremental governing and constitutive equations needed for vibration analysis and solve them numerically using the state-space method (SSM). The results demonstrate the influence of the applied voltage, overcritical circumferential stretch, higher frequency modes, and phase velocity modes on the early development of axisymmetric instability and dielectric breakdown. The existence of the fluid contributes to more reduction in the frequency and phase velocity compared to the fluid-free case due to the added mass effect. Moreover, the results show the role of fluid in the partial self-healing of the soft DEA. A parametric study on specific variables deduces that increasing the thickness of the soft DEA tube reduces the frequency effectively, whereas applying higher voltages causes a thinning in the thickness, leading to the need for thicker tubes.