Wave-Induced Damping of Offshore Structures

ABSTRACT A probabilistic technique for analysis of a guyed tower is presented taking into account the nonlinear behavior of guylines. The wave loading is expressed as an output of normal white noise passing through a filter. Using Ito's method of stochastic differentials, a system of moment equations is developed and is closed at the fourth moment level. The equations are solved in the time domain to obtain the transient and stationary responses. It is shown that the response is non-Gaussian at higher sea states. INTRODUCTION The dynamic analysis procedures for guyed tower platforms have been developed over a decade. Most of the techniques have deterministic formulations (1 – 5). Stochastic methods of analysis have been proved to be of significant value for jacket-type platforms. Spectral analysis requires that the load-structure system be essentially linear. In the case of the guyed tower, the guying system provides the main laterral stiffness. A typical multi-component guyline provides nonlinear stiffness because of geometric nonlinearity, material nonlinearity, load dependence on position, shape and orientation of the cable, and limiting seafloor constraints dependent on cable behavior. Thus, the whole system will have nonlinear stiffness. The response of such a system cannot be completely and reliably estimated using spectral methods. When the waves are realistically modeled as a stochastic process, the estimation of random vibratory behavior of the guyed tower calls for an uncommon but improved methodology. Moreover, with present knowledge, analysis of the nonlinear system under unrestricted random input requires that some sort of approximation be carried out at some stage of the solution. The approximate solution techniques comprise stochastic linearization, perturbation, cumulant neglect and simulation. An iterative method similar to the perturbation method was developed for the second order statistics of theresponse of compliant platforms (6). Linearized frequency domain solutions were shown to be inadequate (7). Systems with nonlinearity in the stiffness exhibit special nonlinear phenomena such as jump. Second order statistics cannot show such results; but it may be seen in higher order statistics of the response (8). Moreover, the assumption of normality neglects the influence of the nonlinearity on the tails of the distribution. Therefore, it is of interest to develop a method which can predict higher order moments and take into account their effect on the distribution. If the nonlinearity in the system is analytical, the method of moment functions is convenient for predicting the statistics of the random dynamic response. When the load is stationary with a rational spectral density, a filter can be devised such that the passage of normal white noise through the filter gives the load as an output. Coordinates described by the filter can be added to the system phase-space and the evolution of response process in the expanded phase-space can be considered as Markov. Ito's rule of stochastic differentials can then be applied to develop differential equations for the moments (9, 10). For a coupled nonlinear system, an infinite hierarchy of equations is formed. This means that equations of a particular order of moment involve moments of the same and higher orders, i.e., with cubic nonlinearity second order moment equations involve moments of the fourth order, the fourth order moment equations involve sixth order moments and so on.