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# How to Play a Disc Brake: A Dissipation-Induced Squeal.

## Abstract

The eigenvalues of an elastic body of revolution, rotating about its axis of symmetry, form a 'spectral mesh'. The nodes of the mesh in the plane 'frequency' versus 'gyroscopic parameter' correspond to the double eigenfrequencies. With the use of the perturbation theory of multiple eigenvalues, deformation of the spectral mesh caused by dissipative and nonconservative perturbations, originating from the frictional contact, is analytically described. The key role of indefinite damping and non-conservative positional forces in the development of the subcritical flutter instability is clarified. A clear mathematical description is given for the mechanism of excitation of particular modes of rotating structures in frictional contact, such as squealing disc brakes and singing wine glasses.

Item Type: Book Section 2008 Kirillov, O. N. How to Play a Disc Brake: A Dissipation-Induced Squeal. English The eigenvalues of an elastic body of revolution, rotating about its axis of symmetry, form a 'spectral mesh'. The nodes of the mesh in the plane 'frequency' versus 'gyroscopic parameter' correspond to the double eigenfrequencies. With the use of the perturbation theory of multiple eigenvalues, deformation of the spectral mesh caused by dissipative and nonconservative perturbations, originating from the frictional contact, is analytically described. The key role of indefinite damping and non-conservative positional forces in the development of the subcritical flutter instability is clarified. A clear mathematical description is given for the mechanism of excitation of particular modes of rotating structures in frictional contact, such as squealing disc brakes and singing wine glasses. Noise and Vibration, 2008, SP-2158, SAE World Congress and Exhibition, April 14-17 2008, Detroit, MI, USA. SAE pa SAE 16 Department of Mechanical Engineering16 Department of Mechanical Engineering > Dynamics and Vibrations 12 Mar 2009 12:53 http://www.sae.org/technical/papers/2008-01-1160 Department of Mechanical Engineering, Dynamics group EP3 XMLEndNoteRDF+XMLSimple MetadataMODSDublin CoreT2T_XMLJSONBibTeXMultiline CSVASCII CitationHTML CitationAtomReference Manager TUfind oder in Google
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