Vibrational Suspension of Light Sphere in a Tilted Rotating Cylinder with Liquid

The dynamics of a light sphere in a quickly rotating inclined cylinder filled with liquid under transversal vibrations is experimentally investigated. Due to inertial oscillations of the sphere relative to the cavity, its rotation velocity differs from the cavity one. The intensification of the lagging motion of a sphere and the excitation of the outstripping differential rotation are possible under vibrations. It occurs in the resonant areas where the frequency of vibrations coincides with the fundamental frequency of the system. The position of the sphere in the center of the cylinder could be unstable. Different velocities of the sphere are matched with its various quasistationary positions on the axis of rotating cavity. In tilted rotating cylinder, the axial component of the gravity force appears; however, the light sphere does not float to the upper end wall but gets the stable position at a definite distance from it. It makes possible to provide a vibrational suspension of the light sphere in filled with liquid cavity rotating around the vertical axis. It is found that in the wide range of the cavity inclination angles the sphere position is determined by the dimensionless velocity of body differential rotation.