  This paper presents a research devoted to the study of instability phenomena
in non-linear model with a constant brake friction coefficient. This paper
outlines the stability analysis and a procedure to reduce and simplify the
non-linear system, in order to obtain limit cycle amplitudes. The center
manifold approach, the multivariable approximants theory, and the alternate
frequency/time domain (AFT) method are applied. Brake vibrations, and more
specifically heavy trucks grabbing are concerned. The modelling introduces
sprag-slip mechanism based on dynamic coupling due to buttressing. The
non-linearity is expressed as a polynomial with quadratic and cubic terms. This
model does not require the use of brake negative coefficient, in order to
predict the instability phenomena. Finally, the center manifold approach, the
multivariable approximants, and the AFT method are used in order to obtain
equations for the limit cycle amplitudes. These methods allow the reduction of
the number of equations of the original system in order to obtain a simplified
system, without loosing the dynamics of the original system, as well as the
contributions of non-linear terms. The goal is the validation of this procedure
for a complex non-linear model by comparing results obtained by solving the
full system and by using these methods. The brake friction coefficient is used
as an unfolding parameter of the fundamental Hopf bifurcation point.
