On the bending coupled natural frequencies of a spinning, multispan Timoshenko shaft carrying elastic disks

Vibration problems of spinning shafts with attached disks occur quite frequently, but until recently the analyses were generally restricted to the flexible-shaft/rigid-disk models, which lost at least two-thirds of the vibrational characteristics to a certain extent. In the present paper, a substructure synthesis technique is applied to the modelling of the bending coupled dynamics of a spinning shaft/disk system with disk flexibility considered. The shaft is treated as a Timoshenko beam. The coupled equations of motion are derived analytically. A numerical study is performed to demonstrate the method developed. The bending coupled natural frequencies, both in view of the shaft transverse vibration and in view of the disk transverse vibration, and the coupled mode shapes are obtained as spin speed varies. The disk flexibility has important effects on the system vibrational behavior, especially at the frequency range near the natural frequencies of single disks. (C) 1999 Academic Press.