Forced beam vibrations of coaxial cylinders separated by a fluid gap of arbitrary size. Inviscid theory and numerical assessment of the fluid forces

Abstract

In this paper, we consider the small-amplitude forced beam vibrations of two coaxial finite-length cylinders separated by an inviscid Newtonian fluid. The three-dimensional fluid problem is solved by introducing a potential function from which the pressure field in the gap is derived. It yields a full analytical expression of the self and cross-fluid forces, which are shown to depend on the Fourier components of the forced vibrations, the aspect ratio, and the radius ratio of the cylinders. Unlike previous theories, the present formulation does not rely on the slender-body approximation nor on the assumption of a narrow gap. Also, the theory is valid whatever the profile of the forced beam vibrations. The theoretical predictions are successfully compared to our numerical simulations, considering clamped-sliding, free-pinned vibration modes and various geometrical configurations (narrow, medium, and wide fluid gaps).