Statistical Research On The Stochastic Green Function Of Ship Near Field

In mathematics,the Green function corresponds to a solution of a Laplace equation with singular points,and satisfies the linear free surface boundary condition along the horizontal direction and the radiation condition at infinity.The main significance of Green function is to solve the boundary integral equation of wave problem.By using proper numerical method,this kind of problem with arbitrary geometry can be solved by Green function on the computer.The statistical study on the near field Green function of ship can be effectively applied to the calculation of ship and marine structures,also can be used to calculate the interaction between the structure and wave.The study has a very important guiding significance on shipbuilding and ship's navigation scheme and its related fields.It can speed up the calculation speed of the ship's hydrodynamic force,shorten the design time and improve the quality of the new ship type.In this paper,a statistical research is conducted on the two dimensional near field Green function.The boundary problem of the Green function is derived,an expression for the stochastic Green function with a single random parameter is obtained,and two distributions are given,which are the distribution of the ship's characteristic length and the joint distribution of the ship's characteristic length and the wave number,and the calculation formula of the confidence interval of the parameters is determined.The main missions are as follows.Firstly,a ship near field two-dimensional non-dimensional Green function of the boundary problem is established based on generalized delta function,the Fourier transform and the inverse transform,the analytical formula of the Green function is derived.The probability distribution of the stochastic Green function and expressions of stochastic Green function are given based on the analytical formula.Finally,the probability distribution of the Green function is solved by using the distribution of the parameters.Secondly,the parameters of the distribution of the ship's characteristic length are determined by the method of using log transform twice,then the distribution density of the ship's length is obtained,and the results are analyzed.Then,according to the empirical formula of the wave spectrum and the relationship between the frequency and the wave number,the joint probability distribution of the ship's length and the wave number is derived,and the error of the calculation of the joint distribution is analyzed.Finally,according to the confidence interval of random variables,the range of the random Green function is studied,and the numerical calculation method of the probability distribution of the ship's near field two-dimensional Green function is given,and the results are analyzed.The innovations of this paper are :(1)a ship near field two-dimensional non-dimensional Green function of the boundary problem is established,and an expression for the stochastic Green function with a single random parameter is obtained;(2)two distributions are given,which are the distribution of the ship's characteristic length and the joint distribution of the ship's characteristic length and the wave number;(3)a calculation method for the confidence interval of stochastic Green function is proposed.