Robust Damping in Self-Excited Mechanical Systems

A technique to optimize the stability of a general mechanical system is outlined. The method relies on decomposing the damping matrix into several component matrices, which may have some special structure or physical relevance. An optimization problem can then be formulated where the ratio of these are varied to either stabilize or make more stable the equilibrium state subject to sensible constraints. For the purpose of this study, we define a system to be more stable if its eigenvalue with largest real part is as negative as possible. The technique is demonstrated by applying it to an introduced non-dimensionalized variant of a known minimal wobbling disc brake model. In this case, it is shown to be beneficial to shift some damping from the disc to the pins for a system optimized for stability. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)