Nonlinear free axisymmetric vibration analysis of dielectric hyperelastic cylindrical shells

Resumo

This work investigates the nonlinear free axisymmetric vibration of a cylindrical shell composed of an isotropic, homogeneous, incompressible, and dielectric hyperelastic material described by the Mooney-Rivlin constitutive model. The external static loading considers two cases: a uniform radial pressure and an axisymmetric radial pressure with the spatial distribution of the first axisymmetric vibration mode. Geometric nonlinearity is incorporated into the analytical model through Sanders-Koiter’s nonlinear shell theory. The Rayleigh-Ritz method, combined with Hamilton’s principle, is used to derive the set of nonlinear equilibrium equations. A comprehensive parametric study examines the effects of initial geometric imperfections, dielectric properties, and static preloading on the nonlinear frequency–amplitude relationship and static equilibrium paths. The results highlight significant changes in both static stability and nonlinear dynamic behavior, depending on the considered parameters and load conditions.