On the influence of external stochastic excitation on linear oscillators with subcritical self-excitation and gyroscopic influence with application to brake squeal
In a linear analysis for brake squeal, an unwanted type of sound in the kHz-range produced during the braking process of vehicles, usually only the stability of the system is examined. However, with the appearance of additional stochastic excitation, the vibration of a linear system with subcritical self-excitation, i.e. having self-excitation but due to damping still an asymptotically stable trivial solution, may be large enough to produce a squeal sound. In this paper, this hypothesis of stochastically reinforced self-excitation is supported by a case study on a wobbling diskmodel for brake squeal, which includes both circulatory and gyroscopic forces. For this example, the Fokker-Planck equation is solved and numerical integrations are performed. A short parameter study is carried out to examine the effect of damping and gyroscopic terms on these stochastically reinforced self-excitation. The results suggest that this possibility should be considered additionally to classical explanations of brake squeal.
Published in: ZAMM : journal of applied mathematics and mechanics = Zeitschrift für angewandte Mathematik und Mechanik, 10.1002/zamm.202000113, Wiley-VCH