The titled problem is studied numerically by finite element calculation. Attention is focused on the behavior of modal interactions when two modes are almost degenerate. In the case when the difference between the numbers of nodal diameters of these two modes is equal to a multiple of the number of the stationary load systems, the frequency loci may merge together (when one of these two modes is a reflected wave) or veer away (when both modes are non-reflected). Otherwise, the natural frequency loci simply cross each other and no instability is induced. When a backward wave meets its complex conjugate at the critical speed, it is found that divergence instability is induced when two times the number of nodal diameters is equal to a multiple of the number of stationary springs.
Vibration and Stability of a Spinning Disk in Contact With Evenly-Spaced Stationary Load Systems
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Chen, J., and Wong, C. (January 1, 1998). "Vibration and Stability of a Spinning Disk in Contact With Evenly-Spaced Stationary Load Systems." ASME. J. Vib. Acoust. January 1998; 120(1): 301–302. https://doi.org/10.1115/1.2893821
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