Shooting and arc-length continuation method for periodic solution and bifurcation of nonlinear oscillation of viscoelastic dielectric elastomers
A majority of dielectric elastomers (DE) developed so far have more or less viscoelastic properties. Understanding the dynamic behaviors of DE is crucial for devices where inertial effects can not be neglected. Through construction of a dissipation function, we applied the Lagrange’s method and theory of non-equilibrium thermodynamics of DE and formulated a physics-based approach for dynamics of viscoelastic DE. We revisited the nonlinear oscillation of DE balloons and proposed a combined shooting and arc-length continuation method to solve the highly nonlinear equations.