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A theoretical analysis is presented for determining the free vibrational and buckling characteristics of the nonhomogeneous, orthotropic, thin-walled, circular cylindrical and conical shells under a hydrostatic pressure and resting on a two-parameter elastic foundation. The basic relations have been obtained for the orthotropic truncated conical shell, the Young's moduli and density of which vary continuously in the thickness direction. By applying the Galerkin method, the buckling hydrostatic pressure and dimensionless frequency parameter of the homogeneous and nonhomogeneous orthotropic truncated conical shells with or without elastic foundations are obtained. Finally, the effects of the Winkler and Pasternak-type elastic foundations, the variations of shell characteristics, the effects of the uonhomogeneity and orthotropy on the critical parameters have been studied. The results are presented in tables, figures and compared with other works.

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This study investigates the frequencies of inhomogeneous orthotropic plates on elastic foundation. The inhomogeneity of orthotropic materials varies linearly with the coordinates of length and thickness. The basic equation is derived applying the Donnell-Mushtari theory and solved using the Galerkin method. The effects of inhomogeneity, Winkler elastic foundation and orthotropy on the frequencies are investigated in detail.