A comprehensive investigation of the free in-plane vibration of a spinning annular disk is presented in this paper. Emphasis is given to the effect of clamping ratio on the natural frequencies and critical speeds of the spinning disk. For a disk with small clamping ratio, the limiting speed at which the disk is allowed to rotate safely is determined by the critical speed of the axisymmetrical mode. Beyond this critical speed divergence instability will be induced. For a disk with large clamping ratio, on the other hand, the speed limit is determined by the critical speed of a mode with a large number of nodal diameters. It is observed that the critical speeds of the modes with nodal diameters approach an asymptotic value as the number of nodal diameters increases. Numerical simulations show that this asymptotic critical speed is independent of the clamping ratio, while it is dependent on the Poisson ratio of the disk.
[1]
On the elastic stability of Coriolis-coupled oscillations of a rotating disc
,
1969
.
[2]
V. Ramamurti,et al.
Dynamic response of an annular disk to a moving concentrated, in-plane edge load
,
1980
.
[3]
G. S. Schajer,et al.
The vibration of a rotating circular string subject to a fixed elastic restraint
,
1984
.
[4]
Jen-San Chen,et al.
In-Plane Stress and Displacement Distributions in a Spinning Annular Disk Under Stationary Edge Loads
,
1997
.
[5]
George G. Adams,et al.
Critical speeds for a flexible spinning disk
,
1987
.