Modeling of the dynamic characteristic of viscoelastic dielectric elastomer actuators subject to different conditions of mechanical load

Subject to a mechanical load or a voltage, a membrane of a dielectric elastomer deforms. As for the deformation mode, the dynamic performance and stability are strongly affected by how mechanical forces are applied. In the current study, by using the Euler-Lagrange equation, an analytical model is developed to characterize the dynamic performance of a homogeneously deformed viscoelastic dielectric elastomer under the conditions of equal-biaxial force, uniaxial force, and pure shear state, respectively. Numerical results are shown to describe the electromechanical deformation and stability. It is observed that the resonant frequency (where the amplitude-frequency curve peaks) has dependencies on the deformation mode, the level of mechanical load, and the applied electric field. When a dielectric elastomer membrane is subject to equal-biaxial force or pure shear state, it undergoes a nonlinear quasi-periodic vibration. An aperiodic motion of the dielectric elastomer system is induced by the boundary condition of a uniaxial force.