In the effort of improving brake noise, recent studies showed increasing encounters with in-plane modes of a rotor for a root cause of a brake noise. Although studies about in-plane modes of a rotor or a disc have been done a lot, a study about the influence of in-plane modes to brake noise has rarely been done. This paper explored the relationship between unstable eigenvalues and rotor mode shapes, focusing on explaining why unstable eigenvalue excited by in-plane modes behaved differently from one caused by out-of-plane modes. Complex eigenvalue analysis was used to assess the instability of a brake corner. This paper showed the way of analytically calculating the sensitivities of unstable eigenvalues about out-of-plane and inplane modes of a rotor. By using the results of sensitivity analysis, it was first discovered that one of the rotor in-plane doublet modes has the opposite sign to the other in the real parts of the sensitivity, and this precludes eliminating the unstable eigenvalues, which are dominated by rotor in-plane modes. However, it was also found that the corresponding unstable eigenvalues could be eliminated if we could separate the frequencies of these modes. Frequency separation of in-plane doublet modes due to disk rotation was examined.

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