Three-dimensional vibration analysis of functionally graded sandwich deep open spherical and cylindrical shells with general restraints

This paper presents three-dimensional (3D) vibration analysis of functionally graded (FG) sandwich deep open shells with general boundary restraints, including open spherical shells and the cylindrical ones. FG sandwich deep open shells composed of homogeneous cores and functionally graded material face sheets with material properties vary continuously through the thickness direction are considered in the present work. The 3D theory of elasticity in conjunction with an energy-based improved Fourier series method are combined to develop the theoretical formulation, in which each displacement of a deep open shell is approximated in terms of a triplicate product of the cosine Fourier series with the addition of certain supplementary terms introduced to remove the potential discontinuities associated with the original displacement and its relevant derivatives at the boundary faces. By using the present method, FG sandwich deep open shells with general boundary restraints, arbitrary geometry parameters, different material distributions and lamination schemes can be solved in a unified form. The accuracy and reliability of the present formulation are validated by comparisons with FEM solutions and those in the literature, and excellent agreements are obtained. Several 3D vibration results of FG sandwich deep open cylindrical and spherical shells with different dimensions in the meridional, circumferential and normal directions are presented for various types of boundary conditions and many representative lamination schemes, which may serve as benchmark solutions for future researchers in assessing two-dimensional approximate theories.