A study on free vibration of a spinning disk

Abstract

Without a logical jump, we have derived the governing equation for free vibration of a spinning circular disk by using the variational formulation based upon the Kirchhoff plate theory and von Karman strain one. It has been found juring the derivation that the governing equation is theoretically valid under the assumption that in-plane deflections are steady and axisymmetric, and that internal forces are linearized while the strains remain nonlinear. The natural frequencies and the critical speeds of a freely spinning disk are obtained approximately and their dependencies on the spinning speed, mode number, and natural frequency of the stationary disk are analyzed.