Prismatic bifurcation of electro-mechanically loaded stacked di-electric cylinders

Study on prismatic bifurcation of two layered stacked di-electric cylinder subjected to electro-mechanical loading has been performed. The stacked cylinders were subjected to uniform pressure at the inner surface of the inner cylinder, coupled with electric loading across the thickness of the cylinder. The cylinders were assumed to have identical material properties, and were considered to be homogeneous and isotropic solid described using the neo-Hookean model. Both axially free tube and axially stretched tube are considered for this analysis. The onset of prismatic diffuse modes for the cylinders was computed by employing linearized incremental equations on the equilibrium configurations of the stacked cylinders, which ultimately yields coupled first order linear differential equations. The effects of cylinder’s thickness on the critical voltage for triggering second mode of prismatic bifurcation was analyzed. The electrical actuation on either of the stacked cylinder results distinct prismatic bifurcation patterns from the same geometry. It was observed that the stacked cylinders may enter diffuse states before the Hessian based stability criteria fails. Moreover, it was found that a cylinder with higher total thickness cylinders requires higher critical voltage to trigger the prismatic bifurcation. The effect of internal pressure on the magnitude of critical voltage was found to be negligible. For the of axially free tube with higher pressurization, the cylinder undergoes snap-through transition instead of prismatic bifurcation.