Closed-form solution for freely vibrating functionally graded thick doubly curved panel-A new generic approach

Abstract

Today, double curvature shell panels are the main parts of each design because their geometrical characteristics provide high strength to weight ratio, aerodynamic form and beauty for the structures such as boats, submarines, automobiles and buildings. Also, functionally graded materials which present multiple properties such as high mechanical and heat resistant, simultaneously, have attracted designers. So, as the first step of any dynamic analysis, this paper concentrates on presenting a high precision and reliable method for free vibration analysis of functionally graded doubly curved shell panels. To this end, panel is modeled based on third order shear deformation theory and both of the Donnell and Sanders strain-displacement relations. A new set of potential functions and auxiliary variables are proposed to present an exact Levy-type close-form solution for vibrating FG panel. The validity and accuracy of present method are confirmed by comparing results with literature and finite element method. Also, effect of various parameters on natural frequencies are studied which are helpful for designers.