Vibrations of cantilevered doubly-curved shallow shells

Vibrational characteristics are determined for a previously unsolved class of problems, that of doubly-curved shallow shells having rectangular planforms, clamped along one edge and free on the other three. The solution procedure uses the Ritz method with algebraic polynomial trial functions. Convergence studies are made, and accurate frequencies and contour plots of mode shapes are presented for various curvature ratios, including spherical, circular cylindrical and hyperbolic paraboloidal shells. Particular emphasis is given to the effect of adding spanwise curvature to shells having chordwise curvature; numerous published references already exist for the case of zero spanwise curvature. The effects of changing aspect ratio, thickness ratio and Poisson's ratio are also studied.