Free and Forced Vibration Analysis of Moderately Thick Functionally Graded Doubly Curved Shell of Revolution by Using a Semi-Analytical Method

This paper describes the free and forced vibration of the doubly curved shells of revolution made of functionally graded (FG) material and constrained by various boundary conditions using a convenient and efficient method based on the Jacobi–Ritz method. The theoretical formulation is established on the basis of the multi-segment partitioning technique and first-order shear deformation theory (FSDT). It is assumed that the material properties of the shell vary smoothly and gradually in the thickness direction according to a typical four-parameter power-law function. At both end positions of the shell, the artificial spring technique is introduced to model the corresponding boundary conditions. Similarly, the connective spring parameters are used to model the continuity conditions between the divided shells. The displacements and rotations of any point of the FG doubly curved shell of revolution including the boundary and connection positions are expanded in form of Jacobi orthogonal polynomials in the meridional direction and Fourier series in the circumferential direction. Then, the dynamic characteristics including natural frequency are easily obtained by the Ritz method. The accuracy and credibility of the present method for free and forced vibration analysis are evidenced through comparison with previous literature and the results of the finite element method (FEM). In addition, through numerical examples, some interesting results about the dynamic behaviors of FG doubly curved shells of revolution with various boundary conditions are investigated, which may be provided as reference data for future study.