Free vibration analysis of moderately thick functionally graded open shells with general boundary conditions

This paper presents the free vibration analysis of functionally graded open shells including cylindrical, conical and spherical ones with arbitrary subtended angle and general boundary conditions. The material properties of the open shells have continuous and smooth variation in the thickness direction based on general four-parameter power-law distributions in terms of volume fractions of the constituents. The formulation is derived by the modified Fourier series in conjunction with Rayleigh–Ritz method according to the first-order shear deformation shell theory. The modified Fourier series is expressed in the form of the linear superposition of a double cosine series and auxiliary functions which are introduced to ensure and accelerate the convergence of the series representations. The comprehensive investigations concerning the convergence and accuracy of the present method are performed by a number of numerical tests and comparisons. Some new results of FGM open shells with elastic restraints are presented. Parametric studies are carried out for FGM open shells with respect to the boundary conditions, material profiles and geometrical parameters.