Random response of catenary moored offshore vessels to non-linear wave forces

Abstract

This paper investigates the response statistics of non-linearly moored vessels to non-linear wave forces. More specifically, the response of a catenary moored vessel to stationary non-Gaussian random excitation is considered in which the equation of motion is of the Duffing type. The approach adopted is based on the assumption that the response may be expressed as a second-order Volterra/Wiener series, that is, including linear and quadratic terms. This allows the response probability density function (pdf) (and mean up-crossing rate) to be calculated using previously developed techniques. The technique used to accomplish this is the Wiener-Hermite functional (WHF) approach. Given that this technique yields coupled integro-differential equations governing the Wiener response kernels which are difficult to solve, an approximate solution procedure is used which is based upon a single-term Galerkin procedure. The relationship of this method to the method of statistical quadratization is investigated, and it is shown that under certain conditions these techniques are mathematically identical. The accuracy of this technique to predict the response pdf is investigated by comparison with numerical simulation.