Free vibration analysis of planar rotating rings by wave propagation

In this paper, a systematic approach for the free vibration analysis of rotating thin rings is presented by wave propagation. The system considered includes a uniform ring and multiple band discontinuities. Neglecting transverse shear, harmonic wave solutions are found for both extensional and inextensional rotating ring models. Frequency spectra and phase diagram are obtained, and the ratio of tangential displacement to radial displacement and cut-off frequencies are determined. Meanwhile, wave reflection and transmission matrices are formulated for cross section area discontinuity condition. These matrices are combined, with the aid of filed transfer matrices, to provide a concise and efficient method for analysing the free vibration problem of rotating rings with multi-span. The computed results are exact since the effects of attenuating wave components are included in the formulation. Two examples are presented to illustrate the validity of the wave propagation approach. This research will be valuable in the free vibration analysis of a solid cage in high speed roller bearing.