This paper presents a theoretical study of vibration localization in single-span, flexible, rotating shafts. A noncircular cross-section of the rotating shaft, leading to dissimilar lateral moments of inertia, can introduce disorder. Internal coupling between the principal directions of vibration is provided by the rotational speed through the gyroscopic moments. It is shown, both analytically and numerically, that directional vibration localization can occur for certain appropriate combinations of disorder and coupling.

Issue Section:
Research Papers
Topics:
Vibration, Rotational inertia
1.
Bolotin, V. V., 1963, Nonconservative Problems of the Theory of Elastic Stability, The Macmillan Co., New York.
2.
Choi, S. H., 1992, “Vibration Localization in Rotating Shafts,” Ph.D. Thesis, University of Michigan, Ann Arbor, Michigan.
3.
Choi
S. H.
,
Pierre
C.
, and
Ulsoy
A. G.
,
1992
, “
Consistent Modeling of Rotating Timoshenko Shafts Subject to Axial Loads
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
114
, No.
2
, pp.
249
–
259
.
4.
Courant, R., and Hilbert, D., 1953, Methods of Mathematical Physics, Vol. 1, Interscience Publishers Inc., New York.
5.
Crandall, S. H., and Brosens, P. J., 1961, “On the Stability of Rotation of a Rotor with Rotationally Unsymmetric Inertia and Stiffness Properties,” ASME Journal of Applied Mechanics, pp. 567–570.
6.
Dimarogonas, A. D., and Paipeties, S. A., 1983, Analytical Methods in Rotor Dynamics, Applied Science Publishers, New York.
7.
Dimentberg, F. M., 1961, Flexural Vibrations of Rotating Shafts, Butterworths, London.
8.
Genta
G.
,
1988
, “
Whirling of Unsymmetric Rotors; A Finite Element Approach Based Upon Complex Coordinates
,”
Journal of Sound and Vibration
, Vol.
124
, No.
1
, pp.
27
–
53
.
9.
Happawana, G. S., Bajaj, A. K., and O. D. I. Nwokah, 1993, “Eigenvalue Veering, Perturbed Bifurcation Theory and Modal Analysis of Mistuned Linear Systems,” C. Pierre and N. C. Perkins, eds., Structural Dynamics of Large Scale and Complex Systems, ASME Publication DE-Vol. 59, pp. 1–13.
10.
Ibrahim
R. A.
,
1987
, “
Structural Dynamics with Parameter Uncertainties
,”
Applied Mech Rev.
, Vol.
40
, pp.
309
–
328
.
11.
Jei
Y. G.
, and
Lee
C. W.
,
1992
, “
Does Curve Veering Occur in the Eigenvalue Problem of Rotors?
”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
114
, pp.
32
–
36
.
12.
Lee, C. W., 1993, Vibration Analysis of Rotors, Kluwer Academic Publishers.
13.
Lee
C. W.
,
Katz
R.
,
Ulsoy
A. G.
, and
Scott
R. A.
,
1988
, “
Modal Analysis of a Distributed Parameter Rotating Shaft
,”
Journal of Sound and Vibration
, Vol.
122
, No.
l
. pp.
119
–
130
.
14.
Leissa
A. W.
,
1974
, “
On a Curve Veering Aberration
,”
Journal of Applied Mathematics and Physics
, Vol.
25
, pp.
99
–
111
.
15.
Perkins
N. C.
, and
Mote
C. D.
,
1986
, “
Comments on Curve Veering in Eigenvalue Problems
,”
Journal of Sound and Vibration
, Vol.
106
, pp.
451
–
463
.
16.
Pierre
C.
,
1988
, “
Mode Localization and Eigenvalue Loci Veering Phenomena in Disordered Structures
,”
Journal of Sound and Vibration
, Vol.
126
, No.
3
, pp.
485
–
502
.
17.
Pierre
C.
,
1990
, “
Weak and Strong Vibration Localization in Disordered Structures: A Statistical Investigation
,”
Journal of Sound and Vibration
, Vol.
139
, No.
l
, pp.
111
–
132
.
18.
Pierre
C.
, and
Dowell
E. H.
,
1987
, “
Localization of Vibrations by Structural Irregularity
,”
Journal of Sound and Vibration
, Vol.
114
, pp.
549
–
564
.
19.
Rao, J. S., 1983, Rotor Dynamics, John Wiley & Sons, New York.
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