Self-excited vibrations in mechanical engineering systems are in general unwanted and sometimes dangerous. There are many systems exhibiting self-excited 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 self-excitation 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 self-excited 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 self-excited 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 self-excited vibrations. The improved models should lead to a better understanding of these unwanted phenomena and possibly also to designs oriented toward their avoidance.
Self-Excited Vibrations and Damping in Circulatory Systems
Dynamics and Vibrations Group,
Numerical Methods in Mechanical Engineering,
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 15, 2013; final manuscript received August 7, 2014; accepted manuscript posted August 11, 2014; published online August 27, 2014. Assoc. Editor: Alexander F. Vakakis.
Hagedorn, P., Eckstein, M., Heffel, E., and Wagner, A. (August 27, 2014). "Self-Excited Vibrations and Damping in Circulatory Systems." ASME. J. Appl. Mech. October 2014; 81(10): 101009. https://doi.org/10.1115/1.4028240
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