Abstract
In the present paper a vibrational fluid-structure system is analyzed with respect to its dynamical stability behavior. In detail, an infinitely long, rigid rotor of circular cross section is considered. It is linearly elastically supported, rotates with constant speed and may perform transversal vibrations in an annulus of arbitrary gap width which is completely filled with a compressible Newtonian fluid.
For the chosen model, a boundary value problem is formulated, whereby the derivation of the equations of motion and the boundary conditions takes into consideration the full fluid-structure interaction.
Because of the absence of external load, there is a stationary state in the form of a constant-speed rotation of the inner cylinder which is in a coaxial position with the cylindrical stator. The bifurcation of the stability problem becomes obvious by introducing a separation of the dependence on the coordinates. On the one hand, so-called Taylor vortices may develop in the fluid flow, while the rotor remains in its coaxial position. On the other hand, coupled fluid cylinder vibrations may occur. In lubrication theory, this phenomenon often is called oil whip resonance. In both cases, an eigenvalue problem for the determination of the stability limit results, which depends on characteristic parameters.
