Abstract
In this study, we apply third-order shear deformation thick shell theory to analytically derive the frequency characteristics of the free vibration of thick spherical laminated composite shells. The equations of motion are derived using Hamilton’s principle of minimum energy and on the basis of the relationships between forces, moments, and stress displacements in the shell.
 
 We confirm the derived equations and analytical results through the finite element technique by using the well-known software packages MATLAB and ANSYS. We consider the fundamental natural frequencies and the mode shapes of simply supported spherical cross-ply (0, 90), (0, 90, 0), and (0, 90, 90, 0) laminated composite shells. Then, to increase accuracy and decrease calculation efforts, we compare the results obtained through classical theory and first-order shear deformation theory.
Highlights
Spherical shells are used mainly for the storage of gas, petrol, liquids, chemicals, and grains
We apply third-order shear deformation thick shell theory to analytically derive the frequency characteristics of the free vibration of thick spherical laminated composite shells
Numerical Results and Discussions The analytical solution developed using the third-order shear deformation theory is employed to validate its applicability in the dynamic analysis of symmetric and nonsymmetric cross-ply spherical laminated shells
Summary
Spherical shells are used mainly for the storage of gas, petrol, liquids, chemicals, and grains They are applied in engineering and transportation, in the structures of motor vehicles, ships, and aircraft (Birman & Byrd, 2007; Koizumi, 1997; Carrera, 2003). A detailed treatment by Baker (Baker, 1961) and Silbiger (Silbiger, 1962) revealed numerous interesting features that served as a test case for shell elements in the third-order shear deformation of thick shell theory. Heated fluid-filled spherical composite shells were studied by (Baker, 1961; Kalnins, 1964; Lamb, 1882; Silbiger, 1962)
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