Vibration of two types of porous FG sandwich conical shell with different boundary conditions

In this paper, in various boundary conditions, the vibration behavior of the two types of porous FG truncated conical sandwich shells is investigated based on the improved high order sandwich shells theory. Two types of porosity are considered in the power law rule to model the FGM properties. In the first type, FG face sheets cover a homogeneous core, and in the second one, the FG core is covered by the homogeneous face sheets. All materials are temperature dependent. By utilizing the Hamilton's energy principle, using the nonlinear von Karman strains in the layers and considering the in-plane stresses and thermal stresses in the core and the face sheets, the governing equations are obtained. A Galerkin method is used to solve the equations with clamped-clamped, clamped-free, and free-free boundary conditions. To validate the results, a FEM software is used and some results are validated with the results in the literatures. Also, Some geometrical parameters, temperature variations and porosity effects are studied. By increasing the length to thickness ratio, temperature, the semi-vertex angle and the radius to thickness ratio, the fundamental frequency parameter decreases in all boundary conditions. In both types of sandwiches for both porosity distributions, by increasing the porosity volume fraction, the fundamental frequency parameters increase. Frequency variation of type-II is lower than type-I in the thermal conditions. And the fundamental frequencies of the clamped-clamped (CC) and clamped-free (C-F) boundary conditions have the highest and lowest values, respectively.