Transverse Vibration of a Rectangularly Orthotropic Spinning Disk, Part 1: Formulation and Free Vibration

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 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.