Subject to an AC voltage, dielectric elastomers (DEs) behave as a nonlinear vibration, implying potential applications as soft dynamical actuators and robots. In this article, by utilizing the Lagrange's equation, a theoretical model is deduced to investigate the dynamic performances of DEs by considering three internal properties, including crosslinks, entanglements, and finite deformations of polymer chains. Numerical calculations are employed to describe the dynamic response, stability, periodicity, and resonance properties of DEs. It is observed that the frequency and nonlinearity of dynamic response are tuned by the internal properties of DEs. Phase paths and Poincaré maps are utilized to detect the stability and periodicity of the nonlinear vibrations of DEs, which demonstrate that transitions between aperiodic and quasi-periodic vibrations may occur when the three internal properties vary. The resonance of DEs involving the three internal properties of polymer chains is also investigated.

Subject to a high voltage, leakage current and induced electrical energy dissipation inevitably occur during the actuation of dielectric elastomers (DEs). In this article, a theoretical model is developed to investigate the dissipative performance of DEs in dynamic actuation. Effects of three different actuation conditions, including DE materials’ viscoelasticity intensity, amplitude of applied voltage, and mechanical tensile force, are considered. Numerical calculations are employed to detect the dynamic dissipative performance of DEs including leakage current, electrical power density, and electrical energy density in certain vibrational periods. Leakage current and induced electrical energy dissipation are enhanced with the enlargement of amplitude of applied voltage and mechanical force, and are suppressed as the intensity of DEs’ viscoelastic creep increases. The electrical energy for dissipation and actuation is also analyzed and compared.

Under an actuation of alternating voltage, dielectric elastomer (DE) based actuators are widely utilized as dynamic devices and robots, accompanying with the possible dynamic instabilities. In this article, based on a deduced dynamics model, we develop an analysis on the dynamic performance and stability evolution of a viscoelastic DE, using the continuous method. Effect of mechanical force and applied voltage are considered, respectively. The spectrum of dynamic deformation with the relevant parameters is presented. The evolution of phase paths is simultaneously provided to detect the dynamic stability of the viscoelastic DE.