Abstract
A Fourier-Bessel series solution is formulated for the non-linear vibration of an unsymmetrically laminated moderately thick shallow spherical shell with its edge elastically restrained against rotation. The effects of transverse shear deformation and rotatory inertia are included in the analysis. The equations of motion are reduced to a set of non-linear ordinary differential equations for the time-dependent coefficients in the series by making use of the Galerkin method. These equations are solved by the method of harmonic balance for undamped free vibrations. The corresponding postbuckling problem is treated as a special case. Numerical results in non-linear free vibration, buckling and postbuckling are presented for various ratios of base radius to thickness and shell rise to thickness, number of layers, material properties and boundary conditions. The present results are compared with available data.
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