An analytical closed-form solution for free vibration and stability analysis of curved sandwich panels made of porous metal-foam core and nanocomposite reinforced face-sheets

Abstract

This paper aims to obtain an analytical solution for free vibration and stability analysis of shallow curved sandwich panels made of a porous metal-foam core and nanocomposites reinforced sheets resting on a Winkler-Pasternak elastic foundation. In this regard, two nanocomposites, carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs) are considered for reinforcing the face-sheets. The governing equations are developed by considering the transversal shear strains based on the first-order shear deformation theory (FSDT). The obtained system of differential equations representing the dynamic equilibrium and compatibility of the proposed curved sandwich panels are solved analytically, using the principal of Galerkin method. In order to examine the results of developed formulation, some benchmark examples are adopted from the existing literature and the obtained results corresponding to the considered examples are compared with those are presented in the references. Using the achieved numerical results in the framework of a comprehensive parametric study, the effects of various material and geometrical factors and also various boundary conditions on the natural frequencies and buckling loads of the proposed sandwich panels are assessed. By performing the extensive parametric study it was observed that several results corresponding to the free vibration and stability of the proposed sandwich panels can be achieved by the present method without spending much time for computations. On the contrary, in order to achieve the similar results using the numerical methods, a time-consuming process is required which can justify the novelty of the present work.