This paper analytically treats the free vibration of coupled, asymmetric disk-spindle systems in which both the disk and spindle are continuous and flexible. The disk and spindle are coupled by a rigid clamping collar. The asymmetries derive from geometric shape imperfections and nonuniform clamping stiffness at the disk boundaries. They appear as small perturbations in the disk boundary conditions. The coupled system eigenvalue problem is cast in terms of “extended” eigenfunctions that are vectors of the disk, spindle, and clamp displacements. With this formulation, the eigenvalue problem is self-adjoint and the eigenfunctions are orthogonal. The conciseness and clarity of this formulation are exploited in an eigensolution perturbation analysis. The amplitude of the disk boundary condition asymmetry is the perturbation parameter. Exact eigensolution perturbations are derived through second order. For general boundary asymmetry distributions, simple rules emerge showing how asymmetry couples the eigenfunctions of the axisymmetric system and how the degenerate pairs of axisymmetric system eigenvalues split into distinct eigenvalues. Additionally, properties of the formulation are ideal for use in modal analyses, Ritz-Galerkin discretizations, and extensions to gyroscopic or nonlinear analyses.

1.
Chivens
D. R.
, and
Nelson
H. D.
,
1975
, “
The Natural Frequencies and Critical Speeds of a Rotating, Flexible Shaft-Disk System
,”
ASME Journal of Engineering for Industry
, Vol.
97
, pp.
881
886
.
2.
Flowers
G. T.
, and
Ryan
S. G.
,
1993
, “
Development of a Set of Equations for Incorporating Disk Flexibility Effects in Rotordynamic Analyses
,”
ASME Journal of Engineering for Gas Turbines and Power
, Vol.
115
, pp.
227
233
.
3.
Klompas
N.
,
1975
, discussion of “
The Natural Frequencies and Critical Speeds of a Rotating, Flexible Shaft-Disk System
,”
ASME Journal of Engineering for Industry
, Vol.
97
, p.
886
886
.
4.
Parker
R. G.
, and
Mote
C. D.
,
1996
a, “
Exact Boundary Condition Perturbation Solutions in Eigenvalue Problems
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
63
, pp.
128
135
.
5.
Parker
R. G.
, and
Mote
C. D.
,
1996
b, “
Exact Perturbation for the Vibration of Almost Annular or Circular Plates
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
63
, pp.
436
445
.
6.
Parker, R. G., and Mote, C. D., Jr., 1997, “Higher-order Perturbation for Asymmetric Disks and Disk-Spindle Systems,” ASME Journal OF Applied Mechanics, manuscript in preparation.
7.
Roach, G. F., Green’s Functions, 1982, Cambridge Univ. Press, Cambridge, UK, p. 156.
8.
Tobias
S. A.
, and
Arnold
R. N.
,
1957
, “
The Influence of Dynamical Imperfection on the Vibration of Rotating Disks
,”
Proc. of the Inst. of Mech. Engineers
, Vol.
171
, pp.
669
690
.
9.
Wilgen
F. J.
, and
Schlack
A. L.
,
1979
, “
Effects of Disk Flexibility on Shaft Whirl Stability
,”
ASME Journal of Mechanical Design
, Vol.
101
, pp.
298
303
.
10.
Yu
R. C.
, and
Mote
C. D.
,
1987
, “
Vibration and Parametric Excitation in Asymmetric Circular Plates Under Moving Loads
,”
ASME Journal of Sound and Vibration
, Vol.
119
, pp.
409
427
.
This content is only available via PDF.
You do not currently have access to this content.