Vibrations of cylindrical shell rotating on rollers

Abstract

Small free vibrations of a rotating closed cylindrical shell of the finite length which is in a contact with rigid cylindrical rollers are considered. Shell edges are or free supported or one of edges is clamped, and another is free. The second case corresponds to conditions of fastening the shell of the centrifugal concentrator. Assumptions of semimomentless shell theory are used. Vibrations modes in the circumferential direction are represented as Fourier series. For any number of uniform distributed rollers the approximate values of the first frequencies are found in explicit form. In case of free supported shell comparison of results obtained by means of approximate semimomentless theory and the classical Kirchhoff-Love theory is performed. From results of calculations follows, that the semimomentless theory can be used for an estimation of the fundamental frequency. The the shell is more thin, the the greater number of the lowest frequencies can be defined under the apprximate formulas. Results of the paper can be used at calculation and designing of the centrifugal concentrators intended for the enrichment of ores.

Keywords:

rotating cylindrical shell, free vibrations, semimomentless theory of shell, eigenvalue problem