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A. Steindl:
"Influence of Kelvin-Voigt Damping on the Existence and Stability of Travelling Wave Solutions";
Talk: MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, Wien/AT; 2012-02-15 - 2012-02-17.

We consider a simple model of a brake, a rigid shaft rotating in an elastic cylinder. Due to the frictional contact between these bodies stick-slip travelling waves occur; also separation zones are possible, if the pressure between the bodies is small. Numerical investigations show, that these travelling waves are mostly unstable, which causes quasiperiodic and chaotic dynamics.
In this talk we investigate the influence of viscous damping on the ex
istence, shape and stability of the travelling wave solutions more closely.
Preliminary calculations indicate, that the smoothening effect may stabilize the travelling waves against the Hopf bifurcation, but it also can destroy the travelling waves in a grazing bifurcation and force steady state solutions.
The presence of the damping terms also changes the structure of the
differential equations for the travelling waves by introducing a small leading coefficient. This singular perturbation also has smoothening effects at the transitions between the different solution regimes.

Dry friction, Travelling waves, stick-slip solutions, singular perturbations