Abstract
This article is dedicated to the free vibrational analysis of a laminated three-phase polymer/GNP/fiber conical shell stiffened with a desired number of intermediate rings. The shell is fabricated from a feeble but low-density polymeric matrix enriched simultaneously with graphene nanoplatelets (GNPs) and aligned fibers. It is assumed that the volume fractions of the matrix, fibers, and GNPs vary along the thickness direction. The laminated shell is modeled according to Murakami’s zig-zag theory and the intermediate rings are considered as rigid structures. The effective elastic constants and the density of the structure are calculated via the Halpin-Tsai model, the rule of mixture, and micromechanical equations. The governing equations, boundary conditions, and compatibility conditions imposed by the ring supports are derived using Hamilton’s principle. A semi-analytical solution is presented to calculate the natural frequencies for various boundary conditions. This solution includes an analytical one in the circumferential direction followed by a numerical solution in the meridional direction. The relationships between the natural frequencies and several parameters are discussed in detail including the boundary conditions, number and location of the rings, weight fractions and dispersion patterns of GNPs and fibers. It is observed that to achieve higher natural frequencies, it is more helpful to distribute the GNPs and fibers far from the middle surface and near the inner and outer surfaces of the shell, especially the inner one.
Published Version
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