An analytical approach to analyze nonlinear dynamic response of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure. Part 1: Governing equations establishment

Abstract

Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique and Galerkin method, this paper deals with the nonlinear dynamic problem of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure by analytical approach. The present novelty is that an approximate three-term solution of deflection taking into account the nonlinear buckling shape is chosen, the nonlinear dynamic second-order differential three equations system is established and the frequency-amplitude relation of nonlinear vibration is obtained in explicit form.