The Determination of nonlinear second-order diffraction forces acting on a ship based on three-dimensional theory

The article discusses the definition of nonlinear diffraction forces of the second order, based on the application of three-dimensional potential theory. To determine them, it is necessary to calculate the potentials of the second order of smallness. The presented solution is new in domestic practice. The problem is solved on the basis of small parameter methods and integral equations taking into account the nonlinear boundary condition on the free surface of the liquid. The paper shows the possibility of calculating the integrals over the free surface directly due to their convergence at an infinite distance from the ship. Nonlinear diffraction forces and moments are determined in the work using various Green's functions: for an infinitely deep fluid and a fluid of limited depth when H -> infinity. The results obtained are in almost complete agreement with each other. The results of calculations of diffraction forces and moments for four different ships are presented. The calculations are presented in comparison with the calculations according to the two-dimensional theory, performed also for the case of an infinitely deep liquid and a liquid of limited depth at large values of ratio H / T. Good agreement of the results with each other is shown. The possibility of calculating nonlinear diffraction forces at arbitrary heading angles is shown.