Abstract
Equations of motion for the large-amplitude flexural vibration of an anti-symmetrically laminated angle-ply shallow spherical shell with rectangular planform are derived by use of Hamilton's principle. The effects of transverse shear and rotatory inertia are included in this study. A solution is formulated in the form of generalized double Fourier series with time-dependent coefficients and satisfies the five boundary conditions along each of simply supported edges. The Galerkin procedure furnishes an infinite system of ordinary differential equations for the time-dependent coefficients. These equations can be truncated to obtain any desired degree of accuracy. The method of harmonic balance is used for a solution. Numerical results for nonlinear free vibrations of isotropic, orthotropic and laminated shallow shells are presented graphically for various shell parameters and lamination geometries. The transverse shear effect on the shell frequency of vibration is discussed in some detail.
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