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In this paper, free vibration analysis of truncated conical shells reinforced with graphene nanoplatelets (GNPs) is studied. The composite shell is considered to be composed of epoxy reinforced with GNPs distributed along the thickness direction based on the various patterns. The shell is modelled based on the first-order shear deformation theory and effective material properties are calculated based on the Halpin-Tsai model along with the rule of mixture. The set of governing equations and boundary conditions are derived using Hamilton’s principle and are solved numerically using generalised differential quadrature method for all possible combinations of clamped, simple and free conditions. Convergence and accuracy of the presented solution are confirmed and influences of various parameters on natural frequencies of the shell are investigated including boundary conditions, semi-vertex angle, circumferential mode number and also total mass fraction, width, thickness and distribution pattern of GNPs. Due to excellent mechanical and thermal properties of GNPs and wide application of conical shells in modern industries such as pressure vessels, aerospace structures and piping, results of this paper can be valuable and useful.

Free vibration analysis of GNP-reinforced truncated conical shells with different boundary conditions