Linear In-Plane Free Vibration of a Rotating Disk
Abstract This paper discusses linear in-plane free vibration of a homogeneous, isotropic, linear visco-elastic rotating disk. Two-dimensional theory of elastico-dynamic is employed to develop the general governing equations of motion. In this analysis, a constant angular velocity is assumed. The wave equations and Bessel Functions of the first and second kind are utilized to obtain the natural frequencies. Natural frequencies are found for a number of modes with several clamping ratios. These natural frequencies were compared with the available established results. Also, the influence of rotational speed and clamping ratio on the natural frequencies and the mode shapes of vibration are determined. The analysis provides information about the elastic stability of the rotating disks for several modes of vibration.