This article deals with the vibrational behavior of composite conical shells (CCSs) reinforced with carbon nanotubes (CNTs) resting on Winkler‐ and Pasternak‐type foundations. A generalized version of the Ambartsumian's first‐order shear deformation theory (FSDT) is here proposed to handle the vibration problems for CCSs reinforced with CNTs, resting on an elastic foundation, while considering a uniform and functionally graded (FG) distribution for the reinforcement phase throughout the shell thickness. The basic equations of the problem are determined and solved in closed form by means of the Galerkin procedure. First, we check for the reliability and accuracy of the proposed formulation with respect to the available literature. It follows a systematic investigation aimed at checking the sensitivity of the structural response to the geometry, the foundation stiffness, the type of distribution, and the volume fraction of CNTs.

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In this study, the non-linear stability of three-layered conical shells with functionally graded core have not been investigated previously. The purpose of this paper is to study this problem. The large deection theory with von KarmanDonnell-type of kinematic non-linearity is used to deduce the basic equations. The basic equations are solved analytically by using superposition and Galerkin methods. The inuences of several parameters on the dimensionless non-linear critical axial loads are discussed.

In this paper, the non-linear (NL) behavior of composite truncated conical shells subjected to dynamic loading is studied. The basic equations are derived using the von Karman-Donnell-type of kinematic nonlinearity. These equations are reduced to a NL dierential equation with the variable coecient using the superposition principle and Galerkin method. The resulting equation is solved numerically using Runge-Kutta method and modied Budiansky-Roth criterion and the values of dimensionless NL critical time parameters are obtained. Finally, the eects of axial loading speed and orthotropy on the dimensionless NL critical time parameters of composite truncated conical shells are investigated.