Efficient Dynamic Analysis of a Combined Spar System via a Frequency Domain Approach

The response of a combined Spar/ risers/mooring lines system is conventionally determined by conducting nonlinear time domain analysis. The system nonlinearity is introduced by the mooring nonlinear force, the friction between the buoyancy-can and the preloaded compliant guide, and the quadratic model of the fluid related damping. Obviously, during the design process, it is important to understand the sensitivity of the Spar responses to various parameters. To a great extent, these objectives cannot be readily achieved by using time domain analysis since, in this context, elements with frequency dependent representation such as the added masses and supplementary damping must be incorporated in the analysis; this may require the use of elaborate convolution techniques. This attribute of the time domain solution combined with the necessity of running a significant number of simulations makes it desirable to develop alternative methods of analysis. In the present paper, a frequency domain approach based on the method of the statistical linearization is used for conducting readily a parametric study of the combined Spar system. This method allows one to account by an equivalent linear damping and an equivalent linear stiffness for the mooring nonlinearity, friction nonlinearity, and the damping nonlinearity of the system. Further, frequency dependent inertia and radiation damping terms in the equations of motion are accommodated. This formulation leads to a mathematical model for the combined system, which involves five-by-five mass, damping and stiffness matrices. In the solution procedure, the equivalent parameters of the linear system are refined in an iterative manner, and by relying on an optimization criterion. This procedure is used to assess the sensitivity of representative Spar system responses to various design parameters. Further, the effect of various design parameters on the combined system response is examined. The environmental loadings considered are of the JONSWAP format of a 100-yr hurricane in the Gulf of Mexico.