AN APPLICATION OF THE STRIP THEORY TO THE NONLINEAR MOTIONS OF SHIPS IN REGULAR WAVES

Based on the previous two dimensional theory which solved the nonlinear motions of cylinders, the present investigation is an attempt to evaluate the nonlinear motions of ships in regular waves by the conventional strip theory. The degree of freedom is increased to five. The second order radiation problems are extended to more interactions between the first order motions. In order to deal with the oblique waves, a special treatment is made to the diffraction and interaction problems and proper phase factors are used in the corresponding potentials.;The first order boundary value problems are solved by the source distribution method in the strip domain. The inhomogeneous free surface condition in the second order problems is regarded as a pressure distribution problem whose solution has been derived. Then the source distribution method is applied to the rest part of the second order problems.;The pressure is evaluated by the Bernoulli equation including the quadratic terms. The forces acting on a ship are obtained by the integration of the pressure along the instantaneous wetted surface of the ship. Finally the motions of the ship are determined up to the second order by the solution of the equations of motions with five degrees of freedom.;Numerical calculations are carried out for a Series-60 hull form in oblique waves. A strong influence of the first order resonances to the second order motions is found. The second order resonance of the heaving and pitching motions is shifted to a longer wave. The different orders of forces are affected by the wave headings in a similar way.;The velocity potential is expanded up to the second order by perturbation theory. The interaction between the first order diffraction and radiation problems are included in the second order potentials. The boundary condition on the body surface is satisfied at its instantaneous position.