Subcritical flutter in the acoustics of friction

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28 Citations (Scopus)

Abstract

Linearized models of elastic bodies of revolution, spinning about their symmetrical axes, possess the eigenfrequency plots with respect to the rotational speed, which form a mesh with double semi-simple eigenfrequencies at the nodes. At contact with friction pads, the rotating continua, such as the singing wine glass or the squealing disc brake, start to vibrate owing to the subcritical flutter instability. In this paper, a sensitivity analysis of the spectral mesh is developed for the explicit predicting the onset of instability. The key role of the indefinite damping and non-conservative positional forces is clarified in the development and localization of the subcritical flutter. An analysis of a non-self-adjoint boundary-eigenvalue problem for a rotating circular string, constrained by a stationary load system, shows that the instability scenarios, revealed in the general two-dimensional case, are typical also in more complicated finite-dimensional and distributed systems
Original languageEnglish
Pages (from-to)2321-2339
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume464
Issue number2097
DOIs
Publication statusPublished - 8 Sep 2008

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