Vibrations of corner point supported shallow shells of rectangular planform

Abstract The first known solution of the title problem is presented. The Ritz method is used, with algebraic polynomials forming the set of trial functions. The condition that all three components of displacement be zero at the four corners is straightforwardly enforced. Numerical studies show that the convergence is relatively slow, requiring more terms than for shells which are completely free. The class of problems studied includes independent, constant curvature in each of the directions parallel to the edges, yielding vibration modes which fall into one of four symmetry classes, with symmetry or antisymmetry of the displacements existing with respect to each of the two symmetry axes of the problem. Detailed results are given for the frequencies and mode shapes of the first two modes of each symmetry class for shells having square planform and circular cylindrical, spherical and hyperbolic paraboloidal curvatures. Accuracy of the results is partially established by comparison with other previously published, accurate results for the corner supported flat square plate.