The paper presents a Hamiltonian approach for extracting the dynamic instability parameters of homogeneously deforming dielectric elastomer actuators subjected to an unequal biaxial prestress, and driven by a suddenly applied electric load. The approach relies on setting up the balance between the kinetic, strain, and electrostatic energy at the point of maximum overshoot in an oscillation cycle. The equation of the stagnation curve, obtained by invoking aforestated statement of energy-balance, is operated upon by the condition of instability to determine the instability parameters. The underlying principles of the approach are elucidated by considering the Ogden family of hyperelastic material models. The approach is however portrayed generically, and hence, can be extended to the other hyperelastic material models of interest. The estimates of the dynamic instability parameters are corroborated by examining the saddle-node bifurcation points in the time-history response obtained by integrating the equation of motion. A parametric study is conducted to bring out the effect of unequal biaxial prestress, and the trends of variation of the critical electric field and the thickness-stretch on the onset of dynamic instability are presented. A quantitative comparison with the static instability parameters reveals that the dynamic instability gets triggered for electric fields that are lower than those corresponding to the static instability. In contrast, the maximum stretch experienced by the actuator at the dynamic instability is significantly higher than that at the static instability. The crucial inferences can find their potential use in the design of DEAs subjected to a transient motion.

This paper reports an energy-based method for the dynamic pull-in instability analysis of a spherical dielectric elastomer (DE) balloon subjected to a quasi-statically applied inflation pressure and a Heaviside step voltage across the balloon wall. The proposed technique relies on establishing the energy balance at the point of maximum stretch in an oscillation cycle, followed by the imposition of an instability condition for extracting the threshold parameters. The material models of the Ogden family are employed for describing the hyperelasticity of the balloon. The accuracy of the critical dynamic pull-in parameters is established by examining the saddle-node bifurcation in the transient response of the balloon obtained by integrating numerically the equation of motion, derived using the Euler–Lagrange equation. The parametric study brings out the effect of inflation pressure on the onset of the pull-in instability in the DE balloon. A quantitative comparison between the static and dynamic pull-in parameters at four different levels of the inflation pressure is presented. The results indicate that the dynamic pull-in instability gets triggered at electric fields that are lower than those corresponding to the static instability. The results of the present investigation can find potential use in the design and development of the balloon actuators subjected to transient loading. The method developed is versatile and can be used in the dynamic instability analysis of other conservative systems of interest.