APPLICATION OF THE RAYLEIGH METHOD TO DETERMINE THE FREQUENCIES OF NATURAL SHELL OSCILLATIONS (ZASTOSUVANNYA METHOD RELEYA DO VYZNACHENNYA CHASTOTY VLASNYKH KOLYVAN OBOLONOK),
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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The approximate Rayleigh method, based on the constancy of the kinetic and potential energies of elastic systems, reduces the calculation of oscillation frequencies of beams and frames to problems involving harmonic oscillations with one degree of freedom. The method is applied to shells and is found to reduce to an even simpler form for shells of revolution when annular sections are deformed according to a cos n theta law n 2, 3, 4, ..., theta is the angle coordinate. For comparison, an approximate calculation of the natural frequencies of a cylindrical shell using the proposed method and slide-rule accuracy yields a frequency of 19.6sec, as compared with a precise calculation which yields 18sec.
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