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

ABSTRACT

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.

KEYWORDS:

• Free vibration
• conical shell
• graphene nanoplatelets
• first-order shear deformation theory
• generalised differential quadrature method

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No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Hassan Afshari

Hassan Afshari received his B.Sc., M.Sc. and Ph.D degrees from the University of Kashan, Iran, in 2009, 2012 and 2017, respectively. He is currently an independent researcher and works as a lecturer in various universities in Iran. His research interests are vibration, rotor dynamics, plates and shells and numerical methods in mechanical engineering.