INFLUENCE OF EXTERNAL PERIODIC OSCILLATION OF A SHALLOW SHELL STRUCTURES MADE OF FGM WITH VARIABLE THICKNESS IN TIME - Fatieieva, Yu. (Computer Science and Applied Mathematics, 2016)
This paper deals with non-linear vibration of shallow spherical shell with initial imperfection made of functionally graded material (FGM) and under an external dynamic loading. The equations of motion, compatibility and stability of the construction are described by the classical theory of shells (Karman theory). It is assumed that the shell base surface as geometrical middle surface. In this paper, we analyze the most popular case of functionally graded shell which top surface is ceramic and bottom surface is metal. The properties of construction are graded in the thickness direction according to the given power low distribution in the terms of volume fraction of the constituents of the construction and initial conditions. Special attention is paid to study of influence external load and material properties on the dynamic behavior construction with given initial conditions. Discussed problem leads to the singular linear non homogeneous second order differential equation with time dependent parameters. An approximate analytical solution for forced oscillations of geometrically non-linear FGM imperfect shallow cylindrical shells with time dependent parameters on the basis of hybrid perturbation WKB approximation method are obtained. The analytical solution was compared with direct numerical integration of initial equation of the problem. For some particular parameters of structure an analytical solutions are in a good enough correlations with direct numerical solutions.