The calculation of hydrodynamic forces acting on a deformable cylinder in free surface

Boundary value problems associated with the deformation of an infinite cylinder in a free surface are formulated. These problems include vibration in still water and deformation due to wave induced forces. The amplitude of deformation is assumed to be small enough for linear theory to be applicable. The deformation itself is assumed to vary sinusoidally along the length of cylinder and arbitrarily girthwise. With the application of Green's theorem for an unbounded fluid, each boundary value problem results in a Fredholm integral equation of the second kind. The integral equation can be solved numerically using a distribution of oscillatory source Green functions on the periphery of the submerged surface. In this technique, Frank's close fit method is extended to treat non-rigid body deformations. Hydrodynamic pressure distributions created by the arbitrary deformation of a cylinder are calculated. The results show that these hydrodynamic pressures are quite dependent on the shape of the deformation pattern and are also quite sensitive to the longitudinal periodicity.