The coupled transverse vibrations of a spinning membrane disk with a central hub

The results of an investigation of the effect of hub coupling on the transverse free vibrations of a spinning membrane disk are presented. The equations of motion are formulated by an energy method and Rayleigh-Ritz procedure. It is found by using assumed modal distributions consisting of the normal modes for the spinning membrane with a rigidly clamped hub that the problem partitions into sub-problems associated with (i) symmetric vibrations involving only the generalized coordinates from the symmetric input modes, (ii) unsymmetric vibrations involving only the input modes with one nodal diameter, and (iii) unsymmetric vibrations involving input modes with more than one nodal diameter. The degree of hub coupling is found to depend primarily on the ratio of the mass of the membrane to the mass of the disk and on the ratio of the radius of the hub to the radius of the disk.