Article: Viscous Theory for the Vibrations of Coaxial Cylinders: Analytical Formulas for the Fluid Forces and the Modal Added Coefficients
This article addresses the small-amplitude forced beam vibrations of two coaxial finite-length cylinders separated by a viscous Newtonian fluid. A new theoretical approach based on an Helmholtz expansion of the fluid velocity vector is carried out, leading to a full analytical expression of the fluid forces and subsequently of the modal added mass and damping coefficients. Our theory shows that the fluid forces are linear combinations of the Fourier harmonics of the vibration modes.