Vibrations of Completely Free Shallow Shells of Curvilinear Planform

Abstract

A method is presented for the free vibration analysis of shallow shells having free edges of arbitrary curvilinear shape. The method of Ritz which was developed for free rectangular plates is extended to the present problem. Components of displacement are expressed as algebraic polynomials. Shells of arbitrary curvature may be treated. Results are obtained for the previously unsolved vibration problems of cylindrical, spherical and hyperbolic paraboloidal shells having free edges of circular and elliptical planform. Convergence of the method is demonstrated. Comparisons with previous solutions are made in the case of zero curvature (i.e., a flat plate). Effects of increasing curvature and ellipticity upon vibration frequencies are examined.