The viscous force and moment acting upon two-dimensional bodies,
undergoing forced oscillations in a fluid at rest, are studied, under the
assumptions of laminar, unseparated flow, small Keulegan-Carpenter number
(K
_c
) and large Stokes parameter (β). Unbounded fluid
conditions are considered first. Previous results by Stokes (1851), for
circular cylinders, and by Molin & Etienne (2000), for non-circular
cylinders in translatory motion, are extended to rotational motion. A complete
viscous damping matrix is derived. Numerical results are given for elliptical
and rectangular shapes. Fluid bounded by a free surface is considered next. The
simple case of a piston wavemaker is first analyzed, with the remarkable result
that the viscous correction to the damping force (due to wave generation) can
be negative. The viscous force is finally derived for ship sections in sway or
roll motion. Numerical results are given for rectangular shapes of different
beam over draft ratios. The practical implications of these results, for the
damping of roll resonance, are discussed.
