Winkler-Pasternak foundation effect on the frequency parameter of FGM truncated conical shells in the framework of shear deformation theory

This work focuses on the vibration behavior of functionally graded (FG) truncated conical shells interacting with the Winkler-Pasternak elastic foundation in the framework of the first-order shear deformation theory (FOSDT). The eigenvalue problem is solved by using Galerkin method. The formulas of the frequencies of FGM truncated cones resting on elastic foundations in the framework of FOSDT are found. Finally, the combined effects of shear strains, material gradient and elastic foundations on the non-dimensional frequency parameters of conical shells with various geometric characteristics in the framework of FOSDT are studied.