Vibration and Stability of a Spinning Disk Under Stationary Distributed Edge Loads

Abstract

The vibration and stability of a spinning disk under conservative distributed edge tractions are studied both numerically and analytically. The edge traction is circumferentially stationary in the space. When the compressive traction is uniform, it is found that no modal interaction occurs and the natural frequencies of all nonreflected waves decrease, while the natural frequencies of the reflected waves increase. When the spinning disk is under distributed traction in the form of cos kθ, where k is a nonzero integer, it is found that the eigenvalue only changes slightly under the edge traction if the natural frequency of interest is well separated from others. When two modes are almost degenerate, however, modal interaction may or may not occur. It is observed that when the difference between the number of nodal diameters of these two modes is equal to ±k, frequency veering occurs when both modes are nonreflected, and merging occurs when one of these two modes is a reflected wave. In applying this rule, the number of nodal diameters of the forward and the reflected wave is considered as negative.