A unified solution for vibration analysis of laminated functionally graded shallow shells reinforced by graphene with general boundary conditions

Abstract

In this paper, a unified method is developed to analyze free vibrations of laminated functionally graded shallow shells reinforced by graphene platelets (GPLs) under arbitrary boundary conditions is proposed. General equations are obtained by the first-order shear deformation theory (FSDT) together with artificial spring technique. By adopting orthogonal polynomials via a Gram-Schmidt process to expand shell displacement fields, Rayleigh-Ritz method is applied in deriving the equations of motion for functionally graded GPL reinforced composite (FG-GPLRC) shallow shells. The accuracy of proposed method is verified through comparing the present results with those from literature. free vibration behaviors of FG-GPLRC shallow shells are studied. The effects of boundary conditions, GPL weight fractions, layer number, and geometric parameters on natural frequencies are investigated. Parametric studies show that variation trends of the natural frequencies of FG-GPLRC shallow shells along with GPL layer number, weight fraction, and geometric properties are similar under different boundary conditions in most cases. However, the frequency values and variation rates are highly dependent on the stiffness values of boundary springs.