The exact equations for the diffraction of plane waves of arbitrary direction by a steadily moving slender ship and for the radiation of waves resulting from the forced oscillations of the same slender ship while moving astern on calm water are formulated. In the radiation problem the speed and the frequency in a coordinate frame moving with the ship are the same as in the diffraction problem. In each of these problems the equations for the first several terms of a two-parameter perturbation expansion are formulated. The parameters are a slenderness parameter, epsilon, e.g. the beam to length ratio, and a motion parameter, i.e. the incident wave amplitude and the hull motion amplitudes for the diffraction and radiation problems respectively. In this formulation it is assumed that the frequency of encounter is O(epsilon to the-1/2) and the forward speed is O(1). For the radiation problem these assumptions lead to strip theory as the lowest order solution. Known solutions for the radiation problem in the heave and pitch modes are described. The difficulties in solving the diffraction problem are discussed. The exciting forces are found in terms of the incident wave potential and the (unknown) diffraction potential. By means of Green's theorem, the boundary conditions for the several potentials, and various vector identities and theorems, the exciting forces are expressed in terms of the incident wave potential and the (known) radiation potentials. Two derivations are given. Particular attention is paid to the complicated non-linear free surface conditions. This result, known previously for zero speed and for forward speed with the frequency of encounter O(1), is called the Haskind relations. The exciting forces given by these extended Haskind relations are compared with previous results for the exciting forces.

  • Corporate Authors:

    Massachusetts Institute of Technology

    Department of Ocean Engineering, 77 Massachusetts Avenue
    Cambridge, MA  United States  02139
  • Authors:
    • McCreight, W R
  • Publication Date: 1973-8-24

Subject/Index Terms

Filing Info

  • Accession Number: 00050907
  • Record Type: Publication
  • Source Agency: Massachusetts Institute of Technology
  • Report/Paper Numbers: PhD Thesis
  • Files: TRIS
  • Created Date: Feb 15 1974 12:00AM