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.

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This paper presents a method to achieve high deformability levels in dielectric elastomer actuators (DEAs) by applying a modulated voltage waveform. The method relies on supplying the electrostatic energy during the specific phase of the oscillation cycle, resulting in the enhanced travel range at a relatively low driving voltage. We consider a standard sandwich configuration of the DE actuator with neo-Hookean material model and outline an energy-based approach for delineating the underlying principles of the proposed method. A comparison of the deformability levels achieved using the quasi-static, Heaviside step, and the modulated input waveforms is presented. Significant reduction in instability voltages together with a considerable increase in the stable actuation limit is observed in the case of the modulated voltage input. The estimates of the stability thresholds are validated by integrating the equation of motion obtained using Hamilton's principle. The effect of energy dissipation is assessed by considering variations in the quality factor. Further, a qualitative comparison with experimental observations is presented highlighting the practical feasibility of the method. This investigation can find its potential use in the design and development of DEAs subjected to a time-dependent motion.