Vibration analysis of truncated conical sandwich shell with porous FG core in different thermal loading

Due to wide application of conical sandwich shells in the advanced industries, it is nessesary to investigate the mechanical behavior of theses structures. In this paper, for the first time, by considering the flexibility of the core in the high order sandwich shells theory, the the vibration behavior of the truncated conical sandwich shells which include a porous FG core and two homogeneous face sheets are investigated in various thermal conditions. Temperature dependent materials are used in the core and the facesheets. The power law rule which modified by considering the two types of porosity volume fractions are applied to model the gradually variation of FGMs. By applying Hamilton's energy principle, considering the in-plane stresses in the core and the faces, and nonlinear von-karman strains for both mechanical and thermal stresses, the governing equations of motion are obtained. A Galerkin procedure are used to solve the equations in a simply supported boundary condition. Uniform, linear and nonlinear temperature distributions are used to model the effect of the temperature changing in the sandwich shell. To verify the results of these work, they are compared with FEM results obtained by Abaqus software and for special cases with the results in literature. Eigen frequencies variations are surveyed versus the temperature changing, geometrical effects, porosities, and some others in the numerical examples.