Squeal is a shrill noise, frequently produced by brakes of cars, planes, trains and others vehicules, which is often a source of great discomfort. For railway brakes, acoustic levels at 1 m from the train can exceed 110 dB, which is not only unpleasant but also induces a health risk for customers and staff in the station. Previous studies suggested that squeal might be reduced by modifying the brake linings. The AcouFren project, lead by the French railway society SNCF, aims to develop tools for designing and specifying low-squeal brake linings. This thesis, part of this project, develops a numerical and experimental study of railway disc brake squeal, particularly for the french high-speed train (TGV) brakes. The experimental study shows the complexity of squeal-related phenomena that can occur during braking, and the variations and the similarities between breaking to a full stop and steady braking. Starting from these observations, expectations with regard to the numerical model are stated: it should be able to reproduce the phenomena of the steady braking. In order to estimate the vibration levels, transient and stationary non-linear dynamics simulations are performed. Once the numerical modelling has been chosen, a solver based on the augmented Lagrangian method is developed. An optimization of the parameters of the method is proposed, which allows significant reduction in computational cost. However, the simulations remain heavily time consuming. This is why a reduction strategy based on the Ritz method and using the complex modes of the system is proposed. The proposed approach is tested on a simple academic model. This allows quantifying the effects of a reduction on a non-linear model destabilized by friction. It is shown that many disturbance phenomena may occur due to the reduction. The only bases of reduction allowing a correct reproduction of the transient and stationary non-linear dynamics of the system are those including all the complex modes in a frequency band as well as the static interface modes. Lastly, the complete numerical strategy is tested on a simplified model of a TGV brake. Compared to the full model, the proposed reduction method reduces the computational cost by a factor of 6. Comparison between simulation and experiment show that both frequencies and vibration levels are predicted with reasonable agreement.
