APPROXIMATION METHOD OF THE DETERMINATION OF FREQUENCIES OF NATURAL VIBRATIONS OF CYLINDRICAL, CONICAL, AND TOROIDAL SHELLS (PRIBLIZHENNYI METOD OPREDELENIYA CHASTOT SOBTVENNYKH KOLEBANII TSILINDRICHESKIKH, KONICHESKIKH I TOROIDALNYKH OBOLOCHEK),
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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Flexural vibrations of shells of revolution are studied, assuming the existence of nodal lines along meridians and parallels. The characteristic equation for determining the square of the natural frequencies is simplified by imposing certain constraints on displacement components. The Ritz method is used with approximation functions which satisfy the boundary conditions, under assumptions that there are no tensional vibrations in the circumferential direction, and no shear in the middle surface. The expediency of the hypotheses used here is verified in investigating the vibrational behavior of cylindrical, conical, and toroidal shells. The advantage of the proposed method is that it leads to simple design formulas.
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