  A potential theory is presented for the problem of two moving cylinders, with
possibly different radii, large motions, immersed in an perfect stagnant fluid.
We show that the fluid force is the superposition of an added mass term,
related to the time variations of the potential, and a quadratic term related
to its spatial variations. We provide new simple and exact analytical
expressions for the fluid added mass coefficients, in which the effect of the
confinement is made explicit. The self-added mass (resp. cross-added mass) is
shown to decrease (resp. increase) with the separation distance and increase
(resp. decreases) with the radius ratio. We then consider the case in which one
cylinder translates along the line joining the centers with a constant speed.
We show that the two cylinders are repelled from each other, with a force that
diverges to infinity at impact. We extend our approach to the case in which one
cylinder is imposed a sinusoidal vibration. We show that the force on the
stationnary cylinder and the vibration displacement have opposite (resp.
identical) axial (resp. transverse) directions. For large vibration amplitudes,
this force is strongly altered by the nonlinear effects induced by the spatial
variations of the potential. The force on the vibrating cylinder is in phase
with the imposed displacement and is mainly driven by the added mass term. The
results of this paper are of particular interest for engineers who need to grab
the essential features associated to the vibration of a solid body in a still
fluid.
