Normal Oscillatory Modes of Rotating Orthotropic Disks

Radial eigenfunctions and mode shapes for rotating isotropic and orthotropic disks. The ratio of the outer radius to the inner radius of the disk is 10.

This Demonstration presents the eigenmodes of rotating isotropic and orthotropic disks. The boundary conditions are fixed at the inner flange and free at the outer edge. It can be shown [1] that the governing wave equation of a spinning disk with the flexural rigidity and the material anisotropy index reduces to the following ordinary differential equation:

,

where

Here, is the radial part of the transversal displacement of the disk. The independent variable is a linear function of the radial distance from the disk center. The parameter is the normalized eigenfrequency, where is the natural frequency of transversal oscillations and is the angular velocity of the disk. All other constant parameters are functions of the geometry and material properties of the disk. Further details on equations, parameters, boundary conditions, and the solution method can be found in [1].

[1] A. Khoshnood and M. A. Jalali, "Normal Oscillatory Modes of Rotating Orthotropic Disks," Journal of Sound and Vibration, 314(1–2), 2008 pp. 147–160.