A stability criterion for parameter-dependent gyroscopic systems is established and three examples are used to illustrate its application to typical engineering problems. In a number of practical situations, the criterion can be used to predict system stability with little actual computation and without solving any eigenvalue problem or approximating the eigenvalue locus. Thus, the criterion provides designers with a quick and accurate tool for assessing the stability consequences of potential design changes.

1.
Done
G. T. S.
, and
Simpson
A.
,
1977
, “
Dynamic Instability of Certain Conservative and Non-Conservative Systems
,”
Journal of Mechanical Engineering Science
, Vol.
19
, No.
6
, pp.
251
263
.
2.
Gohberg, I., Lancaster, P., and Rodman, L., 1982, Matrix Polynomials, Academic Press, New York.
3.
Hryniv, R., and Lancaster, P., 1998, “On the Perturbation of Analytic Matrix Functions,” Integral Equations and Operator Theory, to appear.
4.
Huseyin
K.
, and
Plaut
R. H.
,
1974–1975
, “
Transverse Vibrations and Stability of Systems with Gyroscopic Forces
,”
Journal of Structural Mechanics
, Vol.
3
, No.
2
, pp.
163
177
.
5.
Iwan
W. D.
, and
Moeller
T. L.
,
1976
, “
The Stability of a Spinning Elastic Disk with a Transverse Load System
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
43
, pp.
485
490
.
6.
Lancaster, P., and Kliem, W., 1998, “Comments on Stability Properties of Conservative Gyroscopic Systems,” ASME JOURNAL OF APPLIED MECHANICS, accepted for publication.
7.
Miloslavskii
A. I.
,
1983
, “
Foundations of the Spectral Approach in Nonconservative Problems of the Theory of Elastic Stability
,”
Functional Analysis and Its Applications
, Vol.
17
, pp.
233
235
.
8.
Plaut
R. H.
,
1976
, “
Alternative Formulations for Discrete Gyroscopic Eigenvalue Problems
,”
AIAA Journal
, Vol.
14
, pp.
431
435
.
9.
Renshaw
A. A.
, and
Mote
C. D.
,
1992
, “
Absence of One Nodal Diameter Critical Speed Modes in an Axisymmetric Rotating Disk
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
59
, pp.
687
688
.
10.
Renshaw
A. A.
,
D’Angelo
C.
, and
Mote
C. D.
,
1994
, “
Aerodynamically Excited Vibration of a Rotating Disk
,”
Journal of Sound and Vibration
, Vol.
177
, pp.
577
590
.
11.
Renshaw
A. A.
, and
Mote
C. D.
,
1996
, “
Local Stability of Gyroscopic Systems Near Vanishing Eigenvalues
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
63
, pp.
116
120
.
12.
Renshaw, A. A., 1998, “Stability of Gyroscopic Systems Near Vanishing Eiganvalues,” ASME JOURNAL OF APPLIED MECHANICS, accepted for publication.
13.
Shen
I. Y.
, and
Ku
C.-P. R.
,
1997
, “
A Nonclassical Vibration Analysis of a Multiple Rotating Disk and Spindle Assembly
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
64
, pp.
165
174
.
14.
Sneddon, I. N., 1966, Mixed Boundary Value Problems in Potential Theory, Elsevier, New York.
15.
Tseng
J. G.
,
and Wickert
J. A.
,
1998
, “
Split Vibration Modes in Acoustically-Coupled Disk Stacks
,”
Journal of Vibration and Acoustics
, Vol.
120
, pp.
234
239
.
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