Low-frequency responses of nonlinearly moored vessels in random waves: Coupled surge, pitch and heave motions

The responses of a multi-degree-of-freedom model of a moored vessel are ana lysed, accounting for the hydroelastic interaction between the nonlinear wa ve hydrodynamics and the nonlinear mooring stiffness. A two-scale perturbat ion method developed by Sarkar & Eatock Taylor to determine low-frequency h ydrodynamic forces on a single-degree-of-freedom model of a nonlinearly moo red vessel has been extended to analyse the nonlinear multi-degree-of-freed om dynamics of the system. Surge, heave and pitch motions are considered. T he perturbation equations of successive orders are derived. To illustrate t he approach, semi-analytical expressions for the higher-order hydrodynamic force components have been obtained for a truncated circular cylinder in fi nite water depth. In addition to conventional quadratic force transfer func tions, a new type of higher-order force transfer function is introduced. Th is is used to characterize the hydrodynamic forces on the vessel which aris e due to nonlinearity of the mooring stiffness. These are a type of radiati on force, generated by the nonlinear interaction of the fluid-structure cou pled system. Based on a Volterra series model, the power spectral densities of the new higher-order forces are then derived for the case of Gaussian r andom seas. It is shown that the additional response arising due to nonline ar dynamics of the mooring system can significantly contribute to low-frequ ency drift forces and responses of the vessel. Unlike conventional non-Gaus sian second-order forces which are quadratic transformations of a Gaussian random process, the new higher-order forces arising due to the nonlinear mo oring stiffness are polynomials of a Gaussian random process (up to fourth order for a Duffing oscillator model). This may significantly influence the extreme responses. (C) 2001 Academic Press.