Vibration and stability of thick simply supported shallow shells subjected to in-plane stresses

The effects of higher order deformations on natural frequencies and buckling stresses of a thick shallow shell with reactangular planform subjected to uniaxial and biaxial in-plane stresses are studied. Based on the power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher order shallow shell theory is derived through Hamilton's principle. Several sets of truncated approximate theories which can take into account the complete effects of higher order deformations such as shear deformations with thickness changes and rotatory inertia are applied to solve the vibration and stability problems of a thick shallow shell. Three types of simply supported shallow shells with positive, zero and negative Gaussian curvatures are considered. In order to assure the accuracy of the present theory, convergence properties of the lowest two natural frequencies for the first vibration mode r = s = 1 are examined in detail. The present results are also compared with those of existing theories. In the case of a simply supported shallow shell, buckling stresses can be calculated from the natural frequencies without in-plane stresses. (C) 1999 Academic Press.