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Hopf bifurcations of travelling waves in a brake‐like system
Author(s) -
Steindl Alois
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700813
Subject(s) - disc brake , mechanics , cylinder , slip (aerodynamics) , eigenvalues and eigenvectors , traveling wave , coulomb , hopf bifurcation , brake , classical mechanics , physics , tube (container) , geometry , mathematics , bifurcation , mathematical analysis , engineering , nonlinear system , mechanical engineering , quantum mechanics , thermodynamics , electron
We consider a system composed of an elastic tube, which is fixed at the outer boundary and in frictional contact with a rigid cylinder, rotating inside the tube about the common axis. Under the assumption of Coulomb's friction law at the contact surface between the two bodies several types of rotating slip‐stick and also slip‐stick‐separation travelling waves with different wave numbers can be observed. For a wide range of parameters the linearized system has unstable complex eigenvalues, which cause high frequency oscillations and unpleasant squeal. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)