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A. Steindl:
"Numerical Calculation of Slip-Stick Rotating Waves Caused by Coulomb Friction";
Talk: 8th European Solid Mechanics Conference (ESMC 2012), Graz; 2012-07-09 - 2012-07-13.

We investigate the existence and stability of travelling waves in a
simple model of a brake: A rigid shaft rotates within a fixed
elastic cylinder. At the contact between the bodies we assume
Coulomb friction. Using a 1-mode Galerkin reduction in radial direction
different kinds of Stick-slip travelling waves could be found numerically,
but these solutions turned out to be mostly unstable. Soon after the
loss of stability by Hopf bifurcations irregular motions with a
intricate spatial pattern could be observed.

In order to study the influence of the spatial discretization on the
shape and stability of the travelling waves, we use a finer
discretization in radial direction, using an ansatz with piecewise
linear dependence on the radius. The governing equations for the
travelling waves become a large set of ordinary differential
equations in circumferential direction. Since this system is
extremely stiff, special care has to be taken to reliably solve the
boundary value problem.

Coulomb friction, Travelling waves, singular perturbations