An Analysis of the Free Vibration of a Shallow Spherical Membrane Shell.
NAVAL RESEARCH LAB WASHINGTON D C
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The free vibration of a shallow spherical membrane shell is analyzed using the thin-shell theory developed by Kraus. The secular equation giving the lowest resonant frequencies of such a shell is derived. The normal and tangential modal displacement functions corresponding to these resonant frequencies are found for the case when the shallow spherical shell has a free edge. In addition, an approximate secular equation is derived for the shallow spherical membrane shell with a free edge by using the Rayleigh-Ritz method. Suitable approximate modal displacement functions, corresponding to the resonant frequencies that are determined using this approximate secular equation and satisfying the free-edge boundary condition, are found. Author