Lateral Vibrations of a Rotating Shaft in a Viscous Fluid

Abstract

A rigid rotating cylindrical shaft is vibrating along a diameter in a viscous fluid. Two different cases are investigated through the method of inner and outer expansions. The case of small amplitude vibrations is characterized by the diffusion of vorticity. The coupling of rotation with vibration introduces a normal force, of both inviscid and viscous origins, perpendicular to the direction of oscillation. As rotation increases, the induced steady streaming becomes more skewed and weaker. The case of fast rotation is characterized by the transport of vorticity. Rotation affects both the drag and normal force. The steady torque is increased due to the induction of a steady secondary rotary flow.