An Aproximate Analytical Solution for Nonlinear FGM Shell Structure With Variable in Time Parameters

Abstract

Abstract. This paper deals with the problem of dynamic behavior of thin geometrically imperfect shell structures made of functionally gradient material (FGM) with time dependent parameters. Hybrid asymptotic approach is used to obtain an approximate analytical solution of the problem. The material properties are graded in the thickness direction according to the given law distribution and initial conditions. The non-linear strain-displacement relationships based upon the von Karman theory for moderately large normal deflections. Discussed problem leads to a singular non-linear second order non homogeneous differential equation with variable in time coefficients. An analytical solution by hybrid perturbation-WKB-Galerkin (P-WKB-G) method in some parameters of structure is compared with direct numerical integration results of initial equation of the problem.8654