Accurate Results for Free Vibration of Doubly Curved Shallow Shells of Rectangular Planform (Part.2 Thickness effect)

Abstract

This paper presents a follow-up study of a previous work that deals with the free vibration of moderately thin isotropic shallow shells under general edge conditions. The same semi-analytical method is used in this study for identical shape and degree of curvature in doubly curved geometry, and accurate natural frequencies are tabulated for a wide range of the shell edge conditions. Emphasis is made, however, to present the frequency parameters for the shallow shells with very thin thickness (representative length/shell thickness=100). In numerical experiments, convergence test is made against series terms in the case of very thin shallow shells. Twenty-one sets of frequency parameters are tabulated for three shell shapes (spherical, cylindrical and hyperbolic paraboloidal shells) and two curvature ratios. These two papers (Part.1 and 2) will constitute the accurate standard in the area of shallow shell vibration of rectangular planform and serve for future comparison and practical design purpose.