Non-linear dynamics due to friction induced vibrations in a complex aircraft brake model are investigated. This paper outlines a non-linear strategy, based on the center manifold concept and the rational in order to evaluate the non-linear dynamical behaviour of a system in the neighbourhood of a critical steady-state equilibrium point. In order to obtain time-history responses, the complete set of non-linear dynamic equations may be integrated numerically. But this procedure is both time consuming and costly to perform when parametric design studies are needed. So it is necessary to use non-linear analysis: the center manifold approach and the rational approximants are used to obtain the limit cycle of the non-linear system and to study the behaviour of the system in the unstable region. Results from these non-linear methods are compared with results obtained by integrating the full original system. These non-linear methods appear very interesting in regard to computational time and also necessitate very few computer resources.