Modulation of the dynamic response and stability of dielectric balloon by stretch-dependent dielectric permittivity

The dynamic response of dielectric elastomers is widely used in many functional devices, but current research has neglected the effect of varying dielectric permittivity on their dynamic oscillations and stability. This paper studies the thin-walled dielectric balloon in which the stretch-dependent dielectric permittivity is considered. We obtain the dynamic equation of motion by Hamilton’s principle. Based on the principle of no energy dissipation in conservative systems, we establish energy conservation at the maximum stretching position and at the initial moment, then we investigate the stability in the dynamic case. It is found that a stretch-related dielectric permittivity can increase the critical electric field of the balloon and can also change the mode of electric field instability and modulate the critical stretch value. In the dynamic case, the stretch-dependent permittivity increases the critical electric field by $4%$ when the balloon is only subjected to electric force; moreover, it increases the critical stretch value by $316.68%$ by changing the unstable mode from pull-in instability to snap-through instability. It is hoped that this work will provide new thinking in designing functional devices by using the dynamical response and stability of dielectric elastomers.