Abstract
The effects of changing edge constraints upon the frequencies of shallow shells with rectangular planforms are studied. Attention is focused upon a single edge, with the other three edges remaining completely free. For that edge clamped, simply supported, and free edge conditions are imposed; however, each of these has four possibilities depending upon the existence of either or both types of membrane constraint along the single edge. The Ritz method, assuming algebraic polynomials as displacement functions, is used to obtain accurate results. Frequencies for three types of shallow shells (circular cylindrical, spherical, hyperbolic paraboloidal) are obtained, for two shallowness ratios and two thickness ratios each. Careful attention is paid to the number of rigid body modes (zero frequencies) present, for these enter quite strongly into considerations of the effects of changing edge constraints.
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