The free vibration analysis of a GNP‑reinforced deep thick cylindrical shell surrounded by an orthotropic medium subjected to thermal load

Abstract

In this article, the vibration analysis of a nanocomposite deep thick cylindrical shell surrounded by an ortho- tropic medium subjected to thermal load is studied. It is assumed that the shell is fabricated from a polymeric matrix reinforced with graphene nanoplatelets (GNPs) in which the volume fraction of the GNPs varies along the thickness based on several distribution patterns. The modeling of shell is carried out utilizing a quasi-3D shear theory which includes the thickness stretching. The modeling of the medium is conducted based on the orthotropic Pasternak model. The one-dimensional heat conduction equation is solved analytically to find the temperature profile through the thickness of the shell. Moreover, the dependency of properties of the materials on the temperature is considered. A semi-analytical solution is presented to determine the natural frequencies of the shell and associated mode shapes. The effects of several parameters on the natural frequencies are studied, including the mass fraction and distribution pattern of the GNPs, thermal loading, agglomeration parameters, boundary conditions, and characteristics of the orthotropic medium. Owing to considering the thickness stretch- ing effect, removing shallow shell assumptions, and incorporating the agglomeration of the GNPs, the results of the presented work benefit from high accuracy and can be used in the design and analysis of thin to thick and shallow to deep nanocomposite cylindrical shells.