Random response of a viscoelastic dielectric elastomer spherical balloon

Abstract

The viscoelastic behavior of the dielectric elastomers (DEs) plays an important role in the time-dependent mechanical deformation. The increasingly demands to precise utilities and controls of the DEs are motivating the researchers to insight into the influence of the viscoelasticity on the dynamical response. In this paper, the random response of a DE spherical balloon subjected to electrical and/or mechanical disturbances is analytically studied. Based on a rheological model of two parallel units, the governing equations of the stretch ratio of the deformed and undeformed radius of the spherical balloon are derived from the Lagrange equation. Firstly, the influences of the pressure in balloon and the voltage on the membrane on the equilibrium positions are discussed. The big pressure and high voltage will both induce static instability. Then, by expanding the motion equations around the static equilibrium position, the relation of the resonant frequency with the viscoelasticity are revealed. Finally, an approximation procedure is adopted, which pave the way to adopt the stochastic averaging. The probabilistic density function (PDF) of the stretch ratio around the equilibrium position is obtained. The influences of system parameters, i.e., viscoelasticity, voltage, pressure, on the probability distribution are investigated in detail. The accuracy of the proposed procedure are also been evaluated by the Monte-Carlo simulation (MCS).