Self Excited Vibrations and Damping in Circulatory Systems

Abstract

Selfexcited vibrations in mechanical engineering systems are in general unwanted and sometimes dangerous. There are many systems exhibiting selfexcited vibrations which up to this day cannot be completely avoided, such as brake squeal, the galloping vibrations of overhead transmission lines, the ground resonance in helicopters and others. These systems have in common that in the linearized equations of motion the selfexcitation terms are given by nonconservative, circulatory forces. It has been well known for some time, that such systems are very sensitive to damping. Recently, several new theorems concerning the effect of damping on the stability and on the selfexcited vibrations were proved by some of the authors. The present paper discusses these new mathematical results for practical mechanical engineering systems. It turns out that the structure of the damping matrix is of utmost importance, and the common assumption, namely, representing the damping matrix as a linear combination of the mass and the stiffness matrices, may give completely misleading results for the problem of instability and the onset of selfexcited vibrations. The authors give some indications on improving the description of the damping matrix in the linearized problems, in order to enhance the modeling of the selfexcited vibrations. The improved models should lead to a better understanding of these unwanted phenomena and possibly also to designs oriented toward their avoidance.