ON MEMBRANE FREQUENCIES FOR SPHERICAL SHELL VIBRATIONS
ARMY NATICK LABS MA OFFICE OF THE SCIENTIFIC DIRECTOR
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The membrane solutions for non-symmetric vibration of a spherical dome are studied. The solutions are written in a convenient form, and it is shown how these reduce to the familiar membrane and inextensional solutions in the static limit. This information enables one to perceive several difficulties in finding inextensional frequencies by numerical means and to suggest ways around these difficulties. Also membrane frequencies are found for circumferential wave numbers up through eight by direct calculation and compared with several different approximations. One type of approximation, due to Jeffreys and Jeffreys, gives quite good results. It is seen that earlier work agrees well with these results except for a few frequencies which are not found at all in the present calculations.