Kohn-Kato bounds are determined for the natural frequencies of axial-shear vibrations for a solid circular bar. Through conformal transformation and corresponding modification of the differential equations, this method is extended to the calculation of the natural frequencies of axial shear vibrations for a solid bar having a many-lobed plane, curved boundary. A numerical example is given for an epitrochoidal bar vibrating in the fundamental axial-shear mode. Approximate solutions are developed for the natural frequencies of free vibrations of solid propellant rocket motors with star-shaped perforations.
Technical rept. no. 1,
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