Dynamic modeling of a dielectric elastomeric spherical actuator: an energy-based approach

The present work is concerned with the dynamic modeling of a dielectric elastomeric spherical actuator subjected to an inflation pressure and an electrical DC step voltage across the actuator wall. Herein, we report an alternative method to obtain the static and dynamic instability parameters based on establishing the energy balance principle at the point of maximum stretch in an oscillation cycle. Additionally, we proposed a new energy density function, which accounts the electrostriction phenomenon for a class of an incompressible isotropic dielectric elastomeric material. We first deduce an explicit analytical Lagrange equation of motion based on the Hamiltonian principle of least action for a dielectric elastomeric spherical actuator. Further, a quantitative comparison is presented between the static and dynamic instability parameters. Finally, the numerical results obtained from the developed equation of motion are discussed in line with the parallel results presented in the literature. In summary, the present study brings out the effect of an inflation pressure on the onset of dynamic response in a dielectric elastomeric spherical actuator. In addition, the proposed method is so versatile, and can also be used in other systems of interest.