Abstract
Geometric profile variations always exist in nominally circular rings due to limitations in the manufacturing processes. Such profile variations are known to lead to frequency splitting between pairs of modes which are degenerate in a perfect ring. In this paper, the effects of circumferential profile variations on the in-plane vibration characteristics of such rings are studied using a numerical method. The inner and outer ring surfaces are described in a very general way by Fourier series and the Rayleigh–Ritz method is used to obtain the natural frequencies and mode shapes. Results are presented for a number of example cases which include single- and multiple-harmonic variations in profile. The relationship between the patterns of frequency splitting and the harmonic content of the ring profile is investigated and the most important causes of frequency splitting are identified.
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