DISTRIBUTION OF MAXIMA OF NON-LINEAR ROLLING IN CASE OF COUPLED SWAY AND ROLL MOTIONS OF A FLOATING BODY IN IRREGULAR WAVES

摘要

The so-called Linearize & Match (L&M), which gives a good approximation of the exact distribution of maxima roll angle of non-linear systems, was studied some years ago by Armand and Duthoit (1990) and by Prevosto (2001). The developments within this method were made in the case of single degree of freedom dynamic systems. Moreover, the terms (mass, damping, stiffness) of the non-linear transfer function did not depend on the circular frequency.In this paper, first, the L&M method is improved by adding a last step in the procedure which correct the Gaussian closure technique of the method, secondly is generalized to a coupled sway and roll dynamic system in which the hydrodynamic coefficients are frequency-dependent. The system is modelled by a set of ordinary differential equations in which the non linearity is only in the roll motion. In order to validate the results obtained in this case by the L&M method, a Monte Carlo method with long simulations of the response of the system was carried out. Hence, some aspects of the time domain simulation, based on Cummins equations, are also discussed.