**JVA Abstract**

### Transverse Vibration of a Rectangularly
Orthotropic Spinning Disk -

Part I: Formulation and Free Vibration** **

A. Phylactopoulos and G.G. Adams

Summary

The transverse vibration of a spinning circular disk with
*rectangular* orthotropy is investigated. Two dimensionless
parameters are established in order to characterize the degree of disk
anisotropy and solutions are sought for a range of these parameters.
The orthotropic bending stiffness is transferred into polar coordinates
and is found to differ from a classical formulation for a stationary
disk. A Fourier series expansion is used in the circumferential
direction. Unlike the isotropic disk, the Fourier components
determining the transverse vibration modes of the orthotropic disk do
not separate. This condition results in an *eigenvalue* problem
involving a {\em coupled} set of ordinary differential equations which
are solved by a combination of numerical integration and iteration.
Thus the natural frequencies and normal modes of vibration are
determined. Because each eigenfunction contains contributions from
more than one Fourier component, the normal modes do not possess
distinct nodal diameters or nodal circles. Furthermore, disk
orthotropy causes the natural frequencies corresponding to the
*sine* and *cosine* modes to split; the degree of splitting
decreases as the rotational speed increases.

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