Analysis of vibration characteristics of FGM sandwich joined conical-conical shells surrounded by elastic foundations

The main objective of this paper is focused on the vibration behavior analysis of functionally graded material (FGM) sandwich joined conical-conical shell surround by elastic foundations. In the analysis, four kinds of sandwich distributions, including FGM core and isotropic skins, and isotropic core and FGM skins are considered and the power law distribution is employed to estimate the volume of the constituents. The governing equation of conical shell surround by elastic foundations is established by the first-order shear deformation shell theory and Hamilton's principle. Then generalized differential quadrature (GDQ) method is used to discretize the obtained equations. By using the continuity conditions of displacement, rotation, force and moment between two adjacent shells and the boundary conditions at the end of the connected shell, a set of homogeneous equations are obtained, which control the free vibration of the two joined shell. By comparing the numerical results with the existing solutions in open literature, the validity of the proposed theoretical model is verified. Finally, the influences of sandwich distribution types, gradient indexes, skin-core-skin ratio and boundary conditions on the vibration behavior of FGM sandwich joined conical-conical shell have been investigated. It has found that for different sandwich distribution types, the influences of gradient index on the natural frequency are obvious when the gradient index is minor, but when high values of the gradient index are taken, the gradient index has no significant effect on the natural frequency.