Wave effects on deformable bodies

The linearized frequency-domain analysis of wave radiation and diffraction by a three-dimensional body in a fixed mean position is extended to a variety of deformable body motions. These include continuous structural deflections, and also discontinuous motions which can be used to represent multiple interacting bodies. A general methodology is adopted with the body deflection defined by an expansion in arbitrary modal shape functions, and the response in each mode is obtained as a logical extension of the usual analysis for rigid-body modes. Illustrative computations are presented for the bending of a freely-floating barge, and of a vertical column with cantilever support at the bottom. For these structural deflections the use of orthogonal polynomials is emphasized, as an alternative to the more conventional use of natural modes. Also presented are computations for the motions of two rigid barges connected by a hinge joint, and for a finite array of images used to approximate wall effects on a cylinder in a channel. Results from the latter problem are compared with more analytical solutions, and it is shown that practical results can be obtained for the first-order hydrodynamic force coefficients using only a few images.