Influence of circumferential discontinuity of an elastic foundation on the nonlinear dynamics of cylindrical shells with functionally graded material

Resumo

In this paper we analyze the nonlinear vibrations of cylindrical shells, composed by functionally
graded material, on an elastic foundation with circumferential discontinuity. The equilibrium equations are
obtained from Donnell nonlinear theories and the elastic foundation is represented by Winkler model. The
standard Galerkin's method was applied to discretize the differential partial equations and the perturbation
method is used to describe the modal coupling of the solution that will be used in analysis. The nonlinear
vibration of the shell will be studied through the frequency spectrum and frequency-amplitude relation,
investigating the influence of some system parameters and the proposed modal solution for the transverse
displacement field. Resonance curves for nonlinear forced vibrations and phase portrait are also evaluated,
showing the complex behavior of nonlinear oscillations of shells with discontinuity of the elastic foundation.