Navier type exact analytical solutions for vibrations of thin-walled shallow shells with rectangular planform

Abstract

Exact analytical solutions for the free vibrations of Thin-Walled shallow shells are presented in this work. The shells considered have rectangular planform and two principal constant curvatures. Past treatment of this problem included only one possible case of boundary conditions, and was limited to symmetric modes only. The new solutions address six different cases of in-plane and out-of-plane boundary conditions, and provide an interesting insight into the dynamics of such shells. The formulation may be applied to cylindrical, spherical, elliptical paraboloidal, and hyperbolic paraboloidal shallow shells. Previous works in this field have not addressed the present boundary conditions in exact analytical form.