“…The computational scheme of these methods were developed and the advantages of fractional approximants after the centre manifold approach were discussed; more particularly, the extension of the domain of validity by employing the fractional approximants and the possibility of obtaining an accurate solution even if the associated series expansion diverge was demonstrated. A natural extension of this problem is to show the capability of this centre manifold extension via the fractional approximant for a more complex non-linear mechanical system such as an aircraft brake system where the problem of unstable vibrations in disk brakes has been studied by a number of researchers ( [114], [9], [195], [68], [10], [63], [58], [32], [60], [127] and [68]). As illustrated in Figure 44, an aircraft brake system is composed of a stack of rotating brake discs (rotors) which engage the wheel, and stationary brake discs (stators), which engage the torque tube.…”