The Vibration Analysis of FGM Truncated Conical Shells Resting on Two-Parameter Elastic Foundations

An analytical formulation is presented for the vibration analysis of truncated conical shells made of functionally graded material and resting on the Winkler-Pasternak foundations. It is assumed that the truncated conical shell is a mixture of metal and ceramic that its properties changes as a function of the shell thickness. The governing equations according to the Donnell's theory are solved by Galerkin's method and the fundamental frequencies with or without two-parameter elastic foundation have been found. The effects of the elastic foundations, changing large radius-to-small radius ratio, lengths-to-radius ratio, material composition and volume fraction of constituent materials on the fundamental frequencies of the truncated conical shell are investigated.