A general theory for statistical analysis of nonlinear, second-order forces and motions of compliant offshore structures in short-crested random seas is described. It is shown that the theory is a natural extension of existing theory for the special case of long-crested waves. Similarly as for this special case, the core of the method is the solution of an eigenvalue problem, which IS well suited for numerical analys1s. All the information needed for the statistical analysis IS contained in the obtained eigenvalues and eigenvectors. It is demonstrated that in the case of slowly-varying, second-order forces and motions, the PDF can be given explicitly and is determined completely by the eigenvalues. In contrast to existing theories, in the present paper no restriction is imposed on the bandwidth of either wave energy or d1rectional spread.
Over the last few decades considerable research efforts have been directed toward the problem of characterizing and predicting the second-order, slowly-varying forces and motions of compliant offshore structures in random seas. The major part of these efforts has been Invested on the hydrodynamic side of the problem, and considerable progress has been made. However, parallel to the hydrodynamic investigations, there have also been a development of methods for calculating response statistics. During the past decade or so, a fairly large number of papers have been published dealing with the statistics of second-order, slowly-varying forces and responses of compliant offshore structures. There are probably several (interconnected) reasons for this fact. One may be that design of offshore structures is still largely based on results for unidirectional waves obtained from experimental and/or numerical work. Another reason may be the scarcity of numerical results for the required hydrodynamic coefficients necessary to calculate the nonlinear, second-order forces on three-dimensional floating bodies in shortcrested irregular waves.