Nonlinear dynamic analysis of a cylindrical panel with a discontinuous unilateral elastic base

This work evaluates the nonlinear dynamic behavior and dynamic instability of an imperfect cylindrical panel with a discontinuous unilateral elastic base. The cylindrical panel is described by Donnell’s nonlinear shallow shell theory, being discretized by the Galerkin method, using a previous reduced order model obtained by a perturbation method. It is shown that an efficient modal solution with two degree-of-freedom is sufficient to describe the non-linear softening behavior of the cylindrical panel with a discontinuous elastic base. The Heaviside and the Signum function are used to describe the elastic base domain and the unilateral contact force respectively. The obtained results, using the fourth order Runge-Kutta method, demonstrate the influence of the discontinuous unilateral elastic base and initial geometrical imperfection on the bifurcation diagrams, phase portraits and resonance curves of the cylindrical panel. They demonstrate the important changes in the stable and unstable regions of the nonlinear equilibrium paths and dynamics instability regions due to the unilateral contact constraint and the localized foundation.