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Considerable effort is spent in the design and testing of disk brake systems installed in modern passenger cars. This effort can be reduced if appropriate mathematical–mechanical models are used for studying the dynamics of these brakes. In this context, the mechanism generating brake squeal in particular deserves closer attention. The present paper is devoted to the modeling of self-excited vibrations of moving continua generated by frictional forces. Special regard is given to an accurate formulation of the kinematics of the frictional contact in two and three dimensions. On the basis of a travelling Euler–Bernoulli beam and a rotating annular Kirchhoff plate with frictional point contact the essential properties of the contact kinematics leading to self-excited vibrations are worked out. A Ritz discretization is applied and the obtained approximate solution is compared to the exact one of the traveling beam. A minimal disk brake model consisting of the discretized rotating Kirchhoff plate and idealized brake pads is analyzed with respect to its stability behavior resulting in traceable design proposals for a disk brake.

Rotating plates are used as a main component in various applications. Their vibrations are mainly unwanted and interfere with the functioning of the complete system. The present paper investigates the coupling of disk (in-plane) and plate (out-of-plane) vibrations of a rotating annular Kirchhoff plate in the presence of a distributed frictional loading on its surface. The boundary value problem is derived from the basics of the theory of elasticity using Kirchhoff’s assumptions. This results in precise information about the coupling between the disk and the plate vibrations under the action of frictional forces. At the same time we obtain a new model, which is efficient for analytical treatment. Approximations to the stability boundaries of the system are calculated using a perturbation approach. In the last part of the paper nonlinearities are introduced leading to limit cycles due to self-excited vibrations.

It has become commonly accepted by scientists and engineers that brake squeal is generated by friction-induced self-excited vibrations of the brake system. The noise-free configuration of the brake system loses stability through a flutter-type instability and the system starts oscillating in a limit cycle. Usually, the stability analysis of disk brake models, both analytical as well as finite element based, investigates the linearized models, i.e. the eigenvalues of the linearized equations of motion. However, there are experimentally observed effects not covered by these analyses, even though the full nonlinear models include these effects in principle.The present paper describes the nonlinear stability analysis of a realistic disk brake model with 12 degrees of freedom. Using center manifold theory and artificially increasing the degree of degeneracy of the occurring bifurcation, an analytical expression for the turning points in the bifurcation diagram of the subcritical Hopf bifurcations is calculated. The parameter combination corresponding to the turning points is considered as the practical stability boundary of the system. Basic phenomena known from the operating experience of brake systems tending to squeal prob-

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