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TECHNICAL PAPERS

Bifurcations of Eigenvalues of Gyroscopic Systems With Parameters Near Stability Boundaries

[+] Author and Article Information
A. P. Seyranian

Institute of Mechanics, Moscow State Lomonosov University, Michurynski pr. 1, Moscow 117192, Russiae-mail: seyran@imec.msu.ru

W. Kliem

Department of Mathematics, Technical University of Denmark, Building 303, DK-2800 Kgs. Lyngby, Denmarke-mail: w.kliem@mat.dtu.dk

J. Appl. Mech 68(2), 199-205 (Jun 25, 2000) (7 pages) doi:10.1115/1.1356417 History: Received January 01, 2000; Revised June 25, 2000
Copyright © 2001 by ASME
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References

Thomson, W., and Tait, P. G., 1879, Treatise on Natural Philosophy, Vol. I, Part I, Cambridge University Press, Cambridge, U.K.
Hagedorn,  P., 1975, “Über die Instabilität konservativer Systeme mit gyroskopischen Kräften,” Arch. Ration. Mech. Anal., 58, No. 1, pp. 1–9.
Huseyin,  K., Hagedorn,  P., and Teschner,  W., 1983, “On the Stability of Linear Conservative Gyroscopic Systems,” Z. Angew. Math. Phys., 34, No. 6, pp. 807–815.
Walker,  J. A., 1991, “Stability of Linear Conservative Gyroscopic Systems,” ASME J. Appl. Mech., 58, pp. 229–232.
Barkwell,  L., and Lancaster,  P., 1992, “Overdamped and Gyroscopic Vibrating Systems,” ASME J. Appl. Mech., 59, pp. 176–181.
Seyranian,  A. P., 1993, “Interaction of Vibrational Frequencies of a Gyroscopic System,” Mech. Solids, 28, No. 4, pp. 33–41.
Veselic,  K., 1995, “On the Stability of Rotating Systems,” Z. Angew. Math. Mech., 75, No. 4, pp. 325–328.
Seyranian,  A. P., Stoustrup,  J., and Kliem,  W., 1995, “On Gyroscopic Stabilization,” Z. Angew. Math. Phys., 46, pp. 255–267.
Lancaster,  P., and Zizler,  P., 1998, “On the Stability of Gyroscopic Systems,” ASME J. Appl. Mech., 65, pp. 519–522.
Kliem,  W., and Seyranian,  A. P., 1997, “Analysis of the Gyroscopic Stabilization of a System of Rigid Bodies,” Z. Angew. Math. Phys., 48, No. 5, pp. 840–847.
Mailybaev,  A. A., and Seyranian,  A. P., 1999, “The Stability Domains of Hamiltonian Systems,” J. Appl. Math. Mech., 63, No. 4, pp. 545–555.
Müller, P. C., 1977, Stabilität und Matrizen, Springer-Verlag, Berlin.
Huseyin, K., 1978, Vibrations and Stability of Multiple Parameter Systems, Noordhoff International Publishing, Alphen aan den Rijn.
Merkin, D. R., 1987, Introduction to the Theory of Stability of Motion, Nauka, Moscow.
Vishik,  M. I., and Lyusternik,  L. A., 1960, “The Solution of Some Perturbation Problems for Matrices and Selfadjoint or Non-Selfadjoint Differential Equations I,” Russ. Math. Surv., 15, pp. 1–74.
Lidskii,  V. B., 1966, “Perturbation Theory of Non-Conjugate Operators,” USSR Comput. Math. Math. Phys., 6, No. 1, pp. 73–85.
Moro,  J., Burke,  J. V., and Overton,  M. L., 1997, “On the Lidskii-Vishik-Lyusternik Perturbation Theory for Eigenvalues of Matrices With Arbitrary Jordan Structure,” SIAM J. Matrix Anal. Appl., 18, No. 4, pp. 793–817.
Seyranian,  A. P., 1993, “Sensitivity Analysis of Multiple Eigenvalues,” Mech. Struct. Mach., 21, No. 2, pp. 261–284.
Renshaw,  A. A., and Mote,  C. D., 1996, “Local Stability of Gyroscopic Systems Near Vanishing Eigenvalues,” ASME J. Appl. Mech., 63, pp. 116–120.
Lancaster,  P., and Kliem,  W., 1999, “Comments on Stability Properties of Conservative Gyroscopic Systems,” ASME J. Appl. Mech., 66, pp. 272–273.
Renshaw,  A. A., 1998, “Stability of Gyroscopic Systems Near Vanishing Eigenvalues,” ASME J. Appl. Mech., 65, pp. 1062–1064.
Hryniv,  R. O., Lancaster,  P., and Renshaw,  A. A., 1999, “A Stability Criterion for Parameter Dependent Gyroscopic Systems,” ASME J. Appl. Mech., 66, pp. 660–664.
Parker,  R. G., 1998, “On the Eigenvalues and Critical Speed Stability of Gyroscopic Continua,” ASME J. Appl. Mech., 65, pp. 134–140.
Ziegler, H., 1968, Principles of Structural Stability, Blaisdell, Waltham, MA.
Gohberg, I., Lancaster, P., and Rodman, L., 1982, Matrix Polynomials, Academic Press, San Diego, CA.
Horn, R., and Johnson, C. A., 1985, Matrix Analysis, Cambridge University Press, Cambridge, UK.
Wickert,  J. A., and Mote,  C. D., 1991, “Response and Discretization Methods for Axially Moving Materials,” ASME J. Appl. Mech., 44, pp. S279–S284.

Figures

Grahic Jump Location
Stability (S) and flutter (F) domains in two-dimensional parameter space in the vicinity of the initial point p0
Grahic Jump Location
Normal vector h and vector of variation e at a point of the stability boundary
Grahic Jump Location
Stability and instability domains in the two-dimensional parameter space of the rotating shaft with ω=2 and η=3. S denotes stability, D-divergence, and F-flutter.
Grahic Jump Location
Stability (S) and divergence (D) domains of the axially moving beam

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