Free vibration and stability of hybrid nanocomposite-reinforced shallow toroidal shells using an extended closed-form formula based on the Galerkin method

Abstract

This paper presents an analytical solution for free-vibration and stability analyses of hybrid-composite toroidal shells. The considered hybrid material incorporates the composition of fibers and nanocomposite-reinforced matrix (NCRM) such as carbon nanotubes (CNTs) and graphene nanoplatelets (GPLs). The governing differential equations are extended based on the first-order transverse shear deformation theory (FSDT) and are solved by employing the approximation of Fourier series and Galerkin method. The considered hybrid composite material in the parametric studies are consisted of three layers in which the polymeric matrix are reinforced by CNTs in some layers and reinforced by GPLs in the other layers.

Keywords:

• Toroidal shells
• free vibration
• stability
• first-order transverse shear deformation theory
• closed-form solution
• carbon nanotube
• graphene nanoplatelet

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.