Friction induced vibrations are a major concern in a wide variety of mechanical systems. This is especially the case in aircraft braking systems where the problem of unstable vibrations in disk brakes has been studied by a number of researchers. Solving potential vibration problems requires experimental and theoretical approaches. A nonlinear model for the analysis of mode aircraft brake whirl is presented and developed based on experimental observations. The non-linear contact between the rotors and the stators, and mechanisms between components of the brake system are considered. Stability is analyzed by determining the eigenvalues of the Jacobian matrix of the linearized system at the equilibrium point. Linear stability theory is applied in order to determine the effect of system parameters on stability.

Mechanisms of friction are known as an important source of vibrations in a large variety of engineering systems, where the emergence of oscillations is noisy and can cause severe damage to the system. The reduction or elimination of these vibrations is then an industrial issue that requires the attention of engineers and researchers together. Friction-induced vibrations have been the matter of several investigations, considering experimental, analytical, and numerical approaches. An aircraft braking system is a complex engineering system prone to friction-induced vibrations, and is the subject herein. By considering experimental observations and by evaluating the mechanisms of friction involved, a complete nonlinear model is built. The nonlinear contact between the rotors and the stators is considered. The stability analysis is performed by determining the eigenvalues of the linearized system at the equilibrium point. Parametric studies are conducted in order to evaluate the effects of various system parameters on stability. Special attention will be given to the understanding the role of damping and the associated destabilization paradox in mode-coupling instabilities.

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 nonlinear 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 nonlinear 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 nonlinear 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.

Stability and non-linear dynamics in a complex aircraft brake model are investigated. The non-linear contact between the rotors ands the stators, and mechanisms between components of the brake system are considered. The stability analysis is performed by determining the eigenvalues of the jacobian matrix of the linearized system at the equilibrium point. Parametric studies with linear stability theory is conducted in order to determine the effect of system parameters on stability. In order to obtain time-history responses, the complete set of nonlinear 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 nonlinear 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 nonlinear 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.

This paper presents a research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. The condition of stability is based on the resolution of a generalized eigenvalue problem and the limit cycle amplitude are determined by the center manifold reduction. A model is presented for the analysis of whirl mode vibration in aircraft braking systems. In this study, a non-linear material behaviour of the brake heat stack is considered. This non-linearity is expressed as a polynomial. The model does not require the use of brake negative damping and predicts that instability can occur with a constant brake friction coefficient. The center manifold approach is used to obtain equations for the limit cycle amplitude. The brake friction coefficient is used as unfolding parameter of the fundamental Hopf bifurcation point. The analysis shows that stable and unstable limit cycles can exist for a given constant brake friction coefficient.