Dynamic Response and Stability Analysis with Newton Harmonic Balance Method for Nonlinear Oscillating Dielectric Elastomer Balloons

Subject to various pressure and voltage values, the deformation of a hyperelastic dielectric elastomer membrane may attain different stable and unstable equilibria. In this paper, the neo-Hookean material model is adopted to describe the hyperelastic behavior of a dielectric elastomer membrane. The effects of initial stretch ratio, pressure and voltage on the nonlinear free vibration of a spherical dielectric elastomer balloon are investigated qualitatively and quantitatively. Through a linear stability analysis of the equilibrium states, the safe regime of initial stretch ratio for the deformation of dielectric elastomer balloon is confined. Under specific static driving pressure and voltage, the system oscillates about the stable equilibrium and there is no oscillation in the neighborhood of the unstable equilibrium. Besides, the critical pressure and voltage values are determined. Beyond the critical values, there is no periodic oscillation. Along with the stability analysis, complex dynamical behavior such as drastic change of output regime, sporadic instability and sudden bifurcations can be predicted. By applying the Newton Harmonic Balance (NHB) method for quantitative analysis, the frequency response can be readily predicted. It is found that the nonlinear free vibration frequency decreases with increasing initial stretch ratio and control parameters (pressure and voltage).