The effect of fluid viscosity on coupled tube/fluid vibrations

This paper presents an analytical study of coupled vibration of two coaxial tubes separated by an imcompressible viscous fluid. Tube vibrations are in beam modes and fluid motion is assumed to take place in a plane perpendicular to the axis of the tubes. First, the fluid forces acting on the tubes associated with small tube displacements are obtained in closed form based on the linearized two-dimensional Navier-Stokes equation. Then free and forced vibrations of the coupled tube/fluid system are analyzed. Finally, numerical results for free vibrations of simply supported tubes are presented for several cases to illustrate the effect of various sytem parameters.