The equations of motion for a body performing a precribed periodic oscillation are nondimensionalized with the amplitude of motion and a characteristic velocity amplitude at the driving frequency. A parameter Beta then appears in the (inviscid) equations as the ratio of the amplitude of motion to the wave-length of a free wave corresponding to the driving frequency. The parameter is small even for large amplitudes of motion if the driving frequency is sufficiently small. The velocity potential can then be expanded and a series of boundary-value problems derived for the successive terms of the expansion. The problem is basically a perturbation about the low frequency of "rigid wall" first-order boundary-value problem and requires a far-field for matching with the singular inner solution. The inner problems are all Neumann boundary-value problems with time appearing as a parameter, i.e., the geometry changes with time. The far-field is the usual linearized free-surface boundary condition, homogeneous through order Beta squared log Beta for heave and roll and Beta squared for sway. The inner solutions are found by mapping the general geometry onto a circle and expressing the singularity strengths as Fourier time series. These are then matched with the appropriate far-field wavemaking singularities. The matching identifies the arbitrary constant of the inner Neumann problem. The matching also imposes gradually stronger terms on the inner problem that are homogeneous with respect to the free-surface boundary condition. The analysis was applied to heave, sway, and roll. The results indicate that within the range of validity of the analysis, heave and sway show little nonlinear amplitude dependence. The nonlinear amplitude dependence of the damping in roll can be large, but is apparently still dominated by the viscous damping effects at low frequencies.

  • Corporate Authors:

    Massachusetts Institute of Technology

    Department of Ocean Engineering, 77 Massachusetts Avenue
    Cambridge, MA  United States  02139
  • Authors:
    • Oakley Jr, O H
  • Publication Date: 1972-8

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Filing Info

  • Accession Number: 00048369
  • Record Type: Publication
  • Source Agency: Massachusetts Institute of Technology
  • Report/Paper Numbers: PhD Thesis
  • Files: TRIS
  • Created Date: Nov 14 1973 12:00AM