Depending on the speed of rotation, a gyroscopic system may lose or gain stability. The paper characterizes the critical angular velocities at which a conservative gyroscopic system may change from a stable to an unstable state, and vice versa, in terms of the eigenvalues of a high-order matrix pencil. A numerical method for evaluation of all possible candidates for such critical velocities is developed.
Issue Section:
Technical Papers
1.
Parker
, R. J.
, 1998
, “On the Eigenvalues and Critical Speed Stability of Gyroscopic Continua
,” ASME J. Appl. Mech.
, 65
, pp. 134
–140
.2.
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
.3.
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
.4.
Barkwell
, L.
, and Lancaster
, P.
, 1992
, “Overdamped and Gyroscopic Vibrating Systems
,” ASME J. Appl. Mech.
, 59
, pp. 176
–181
.5.
Duffin
, R. J.
, 1955
, “The Rayleigh-Ritz Method for Dissipative or Gyroscopic Systems
,” Q. Appl. Math.
, 18
, pp. 215
–221
.6.
Lancaster
, P.
, and Zizler
, P.
, 1998
, “On the Stability of Gyroscopic Systems
,” ASME J. Appl. Mech.
, 65
, pp. 519
–522
.7.
Walker
, J.
, 1988
, “Pseudodissipative Systems, I: Stability of Generalized Equilibria
,” ASME J. Appl. Mech.
, 55
, pp. 681
–686
.8.
Walker
, J. A.
, 1991
, “Stability of Linear Conservative Gyroscopic Systems
,” ASME J. Appl. Mech.
, 58
, pp. 229
–232
.9.
Veselic´
, K.
, 1995
, “On the Stability of Rotating Systems
,” Z. Angew. Math. Mech.
, 75
, pp. 325
–328
.10.
Hryniv
, R.
, and Lancaster
, P.
, 2001
, “Stabilization of Gyroscopic Systems
,” Z. Angew. Math. Mech.
, 81
, pp. 675
–681
.11.
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
.12.
Seyranian
, A.
, Stoustrup
, J.
, and Kliem
, W.
, 1995
, “On Gyroscopic Stabilization
,” Z. Angew. Math. Phys.
, 46
, pp. 255
–267
.13.
Afolabi
, D.
, 1995
, “Sylvester’s Eliminant and Stability Criteria for Gyroscopic Systems
,” J. Sound Vib.
, 182
, pp. 229
–244
.14.
Turnbull, H. W., 1944, Theory of Equations, Oliver and Boyd, Edinburgh, UK.
Copyright © 2003
by ASME
You do not currently have access to this content.