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TECHNICAL PAPERS

Stability Boundaries of a Conservative Gyroscopic System

[+] Author and Article Information
G. M. L. Gladwell

Department of Civil Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

M. M. Khonsari, Y. M. Ram

Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70806

J. Appl. Mech 70(4), 561-567 (Aug 25, 2003) (7 pages) doi:10.1115/1.1574062 History: Received October 07, 2001; Revised April 29, 2002; Online August 25, 2003
Copyright © 2003 by ASME
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References

Parker,  R. J., 1998, “On the Eigenvalues and Critical Speed Stability of Gyroscopic Continua,” ASME J. Appl. Mech., 65, pp. 134–140.
Ahmadian,  M., and Inman,  D. J., 1986, “Some Stability Results for General Linear Lumped-Parameter Dynamic Systems,” ASME J. Appl. Mech., 53, pp. 10–14.
Barkwell,  L., Lancaster,  P., and Marcus,  A. S., 1992, “Gyroscopically Stabilized Systems: A Class of Quadratic Eigenvalue Problems With Real Spectrum,” Can. J. Math., 44, pp. 42–53.
Barkwell,  L., and Lancaster,  P., 1992, “Overdamped and Gyroscopic Vibrating Systems,” ASME J. Appl. Mech., 59, pp. 176–181.
Duffin,  R. J., 1955, “The Rayleigh-Ritz Method for Dissipative or Gyroscopic Systems,” Q. Appl. Math., 18, pp. 215–221.
Lancaster,  P., and Zizler,  P., 1998, “On the Stability of Gyroscopic Systems,” ASME J. Appl. Mech., 65, pp. 519–522.
Walker,  J., 1988, “Pseudodissipative Systems, I: Stability of Generalized Equilibria,” ASME J. Appl. Mech., 55, pp. 681–686.
Walker,  J. A., 1991, “Stability of Linear Conservative Gyroscopic Systems,” ASME J. Appl. Mech., 58, pp. 229–232.
Veselić,  K., 1995, “On the Stability of Rotating Systems,” Z. Angew. Math. Mech., 75, pp. 325–328.
Hryniv,  R., and Lancaster,  P., 2001, “Stabilization of Gyroscopic Systems,” Z. Angew. Math. Mech., 81, pp. 675–681.
Seyranian,  A. P., and Kliem,  W., 2001, “Bifurcations of Eigenvalues of Gyroscopic Systems With Parameters Near Stability Boundaries,” ASME J. Appl. Mech., 68, pp. 199–205.
Seyranian,  A., Stoustrup,  J., and Kliem,  W., 1995, “On Gyroscopic Stabilization,” Z. Angew. Math. Phys., 46, pp. 255–267.
Afolabi,  D., 1995, “Sylvester’s Eliminant and Stability Criteria for Gyroscopic Systems,” J. Sound Vib., 182, pp. 229–244.
Turnbull, H. W., 1944, Theory of Equations, Oliver and Boyd, Edinburgh, UK.

Figures

Grahic Jump Location
A particle in a rotating frame
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A continuous gyroscopic system: (a) a rotating shaft, and (b) a free-body diagram for a typical element
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Eigenvalue change due to a small perturbation in ω near the stability boundaries: (a) losing stability, and (b) gaining stability
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Root loci for two nonconjugate eigenvalues

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