pb-2 Ritz formulation for flexural vibration of shallow cylindrical shells of rectangular planform

This paper presents a free flexural vibration analysis of shallow cylindrical shells of rectangular planform with arbitrary combinations of free, simply supported and clamped boundaries. The pb-2 Ritz method previously used in the plate analysis by one of the authors is now extended to shallow shell studies. The Ritz approach, along with the in-plane and transverse displacements assumed in the form of orthogonal polynomials, is used to formulate the problems. Numerical results for the vibration frequencies for wide ranges of aspect ratio, shallowness ratio and thickness ratio are presented. Several selected contour plots of the mode shapes for six different combinations of boundary conditions are presented. As usual, the accuracy of the present method is illustrated by convergence tests and comparison with the well established results from the literature.