Plates, cylindrical and spherical shells, and in general, doubly curved shell panels are the main parts of each new structural design because their geometrical characteristics give them high strength to weight ratio. Moreover, requiring high mechanical and heat resistant materials leads engineers to use functionally graded material to achieve both of these characteristics. Hence, having a reliable high precision method for free vibration analysis of such shell panels is the first step of each dynamical analysis. This paper used a set of potential functions and auxiliary variables to present an exact Levy-type closed-form solution for free vibration of a doubly curved FG shell panel. The first-order shear deformation theory beside both the Donnell and Sanders strain-displacement relations are considered for mathematical modeling. The results of the present method are checked with the literature and a finite element analysis in which good agreement is observed. Also, a benchmark study is presented that will be useful for future researches.
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