A Gaussian and non-Gaussian stochastic linear model of a submerged cable forced by random load

The displacement of the cable structure is governed by a nonlinear system of partial differential equations. When random loads force the cable, its displacement is necessarily random. In this case the knowledge of the displacement time history is meaningless in comparison to the knowledge of its probability density function (pdf). Analytically, this pdf can be calculated only by solving the nonlinear set of differential equations. A numerical approximation of this pdf can be found by the knowledge of the displacement statistic moments. They can be approximately provided by a Monte Carlo technique, but this causes a very heavy computational burden. Aim of this article is the study of a model which predicts the dynamic motion of a submerged mooring cable having one end anchored at the sea bottom and the other end joined to a buoy forced by the wave load. A non-linear one degree of freedom model predicting the displacement of the buoy and two different stochastic linear models are provided. A Gaussian and non-Gaussian stochastic linearization methods are employed to substitute this nonlinear equation with two new equivalent linear relationships. These linear models have the possibility to describe the statistic properties of the free end motion of the cable directly exploiting the theory of the random linear systems.