The combined influences of heterogeneity and elastic foundations on the nonlinear vibration of orthotropic truncated conical shells

Abstract The aim of the present paper is to study the nonlinear vibration of heterogeneous orthotropic truncated conical shells resting on the Winkler–Pasternak elastic foundations. The formulation is based on the Donnell shell theory, exponential-law distribution of orthotropic material properties and von Karman geometric nonlinearity. The basic equations are reduced to a time dependent geometrical nonlinear differential equation and solved using homotopy perturbation method (HPM). Finally, the influences of elastic foundations, heterogeneity, material orthotropy and shell characteristics on the nonlinear vibration of the truncated conical shell are studied.

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