The influence of non-homogeneity on the frequency–amplitude characteristics of laminated orthotropic truncated conical shell

In this study, the non-linear vibration of laminated non-homogenous orthotropic truncated conical shell is investigated. It is assumed that the Young’s moduli, shear modulus and density of the layers of the shell vary exponentially through the thickness direction. The basic equations of laminated non-homogenous orthotropic truncated conical shells are derived using the large deformation theory with von Karman–Donnell-type of kinematic non-linearity. The non-linear basic equations are reduced to the non-linear differential equation depending on the time using the superposition principle and Galerkin method. This equation is solved using semi-inverse method and is found the frequency–amplitude relationship. Finally, carrying out some computations, the effects of non-homogeneity, number and ordering of layers, and conical shell characteristics on frequency–amplitude characteristics have been studied.