An analytical study on the effect of rigid body translational degree of freedom on the vibration characteristics of elastically constrained rotating disks

This study concerns the linear vibration behavior of annular spinning disk whose inner boundary is free to move in the axial direction while the body of the disk is constrained by a space fixed linear spring. It is shown, using analytical techniques based upon a three mode approximation, that constraining a spinning disk, free to have rigid body translation, with one space fixed spring does not change the critical speeds. Using an analysis, based on a two-mode approximation, the stability characteristics of a guided spinning disk due to the interaction between a rigid body translational mode and a forward or backward or reflected traveling wave are studied. It is shown that the interaction between the rigid body translational mode and a forward or backward traveling wave does not induce instability. In contrast to this situation it is shown that when the rigid body translational degree of freedom interacts with a reflected wave, depending on the speed and the stiffness of the spring, it may induce instability.