The response and natural frequencies for the linear and nonlinear vibrations of rotating disks are given analytically through the new plate theory proposed by Luo in 1999. The results for the nonlinear vibration can reduce to the ones for the linear vibration when the nonlinear effects vanish and for the von Karman model when the nonlinear effects are modified. They are applicable to disks experiencing large-amplitude displacement or initial flatness and waviness. The natural frequencies for symmetric and asymmetric responses of a 3.5-inch diameter computer memory disk as an example are predicted through the linear theory, the von Karman theory and the new plate theory. The hardening of rotating disks occurs when nodal-diameter numbers are small and the softening of rotating disks occurs when nodal-diameter numbers become larger. The critical speeds of the softening disks decrease with increasing deflection amplitudes. [S0739-3717(00)02004-3]

1.
Lamb
,
H.
, and
Southwell
,
R. V.
,
1921
, “
The vibrations of a spinning disc
,”
Proc. R. Soc. London, Ser. A
,
99
, pp.
272
280
.
2.
Southwell
,
R. V.
,
1992
, “
On the free transverse vibrations of a uniform circular disc clamped at its center, and on the effects of rotation
,”
Proc. R. Soc. London, Ser. A
,
101
, pp.
133
153
.
1.
Kirchhoff
,
G.
,
1850
, “
Uber das Gleichgewicht und die Bewegung einer elastischen Scheibe
,”
J. Reine Angew. Math.
,
40
, pp.
51
88
;
2.
Kirchhoff
,
G.
,
1850
, “
Ueber die Schwingungen einer kreisformigen elastischen Scheibe
,”
Pogg. Ann.
,
81
, pp.
258
264
.
1.
Mote
, Jr.,
C. D.
,
1965
, “
Free vibration of initially stressed circular plates
,”
J. Eng. Ind.
,
87
, pp.
258
264
.
2.
Iwan
,
W. D.
, and
Moeller
,
T. L.
,
1976
, “
The stability of a spinning elastic disk with a transverse load system
,”
J. Appl. Mech.
,
43
, pp.
485
490
.
3.
von Freudenreich
,
J.
,
1925
, “
Vibration of steam turbine discs
,”
Engineering
,
199
, pp.
2
4
and 31–34.
4.
Campbell
,
W.
,
1924
, “
The protection of steam-turbine disk wheels from axial vibration
,”
Trans. ASME
,
46
, pp.
31
160
.
5.
Tobias
,
S. A.
,
1957
, “
Free undamped nonlinear vibrations of imperfect circular disks
,”
Proc. Inst. Mech. Eng.
,
171
, pp.
691
701
.
6.
Nowinski
,
J. L.
,
1964
, “
Nonlinear transverse vibrations of a spinning disk
,”
J. Appl. Mech.
,
31
, pp.
72
78
.
7.
Nowinski
,
J. L.
,
1981
, “
Stability of nonlinear thermoelastic waves in membrane-like spinning disks
,”
J. Thermal Sci.
,
4
, pp.
1
11
.
8.
Advani
,
S. H.
,
1967
, “
Stationary waves in a thin spinning disk
,”
Int. J. Mech. Sci.
,
9
, pp.
307
313
.
9.
Advani
,
S. H.
, and
Bulkeley
,
P. Z.
,
1969
, “
Nonlinear transverse vibrations and waves in spinning membrane discs
,”
Int. J. Non-linear Mech.
,
4
, pp.
123
127
.
10.
Renshaw
,
A. A.
, and
Mote
, Jr.,
C. D.
,
1995
, “
A perturbation solution for the flexible rotating disk: Nonlinear equilibrium and stability under transverse loading
,”
J. Sound Vib.
,
183
, pp.
309
326
.
11.
Luo, A. C. J., 1999, “An approximate theory for geometrically-nonlinear thin plates,” Int. J. Solids Struct., in press.
12.
Byrd, P. F., and Friedman, M. D., 1954, Handbook of Elliptic Integrals for Engineers and Physicists, Springer-Verlag, Berlin.
You do not currently have access to this content.