This paper deals with stability problems of linear gyroscopic systems with finite or infinite degrees-of-freedom, where the system matrices or operators depend smoothly on several real parameters. Explicit formulas for the behavior of eigenvalues under a change of parameters are obtained. It is shown that the bifurcation (splitting) of double eigenvalues is closely related to the stability, flutter, and divergence boundaries in the parameter space. Normal vectors to these boundaries are derived using only information at a boundary point: eigenvalues, eigenvectors, and generalized eigenvectors, as well as first derivatives of the system matrices (or operators) with respect to parameters. These results provide simple and constructive stability and instability criteria. The presented theory is exemplified by two mechanical problems: a rotating elastic shaft carrying a disk, and an axially moving tensioned beam.
Bifurcations of Eigenvalues of Gyroscopic Systems With Parameters Near Stability Boundaries
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Jan. 1, 2000; final revision, June 25, 2000. Associate Editor: N. C. Perkins. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Seyranian, A. P., and Kliem, W. (June 25, 2000). "Bifurcations of Eigenvalues of Gyroscopic Systems With Parameters Near Stability Boundaries ." ASME. J. Appl. Mech. March 2001; 68(2): 199–205. https://doi.org/10.1115/1.1356417
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