Stability Analysis of a Spinning Elastic Disk Under a Stationary Concentrated Edge Load

Abstract

The natural frequencies and stability of a spinning elastic disk subjected to a stationary concentrated edge load are investigated both numerically and analytically. It is found that a stationary, conservative, compressive edge load decreases the natural frequencies of the forward and backward traveling waves, but increases the natural frequency of the so-called reflected wave. It is also found that the significance of the effect of the conservative edge load on the natural frequencies and stability of the spinning disk is solely through the transverse component of the edge load on the boundary, and not through the membrane stress field it produces inside the disk. In addition, the compressive edge load induces a stationary-type instability before the critical speed, and induces a merged-type instability after the critical speed when a reflected wave meets a forward or a backward wave. The expression for the derivative of the eigenvalues of the spinning disk with respect to the edge load is derived to verify the numerical results.