Coupled Analysis of a Spar Structure: Monte Carlo and Statistical Linearization Solutions

Abstract

The response of a combined dynamic system consisting of a Spar, a mooring line system, and top tension risers is presented. The top tension of a riser is provided by a buoyancy can that is laterally supported by a preloaded compliant guide. The overall system is nonlinear due to the mooring line restoring force, the friction between the buoyancy cans and the compliant guides, and the friction between the risers and the guides at the Spar keel. The friction between the Spar and the riser system is captured by a Coulomb model, whereas the stiffness of the mooring line system is accounted for by using a regression analysis of pertinent load versus displacement data. The combined model is numerically integrated using input time histories of force and moment that are compatible with a random representation (Jonswap spectrum) of a typical extreme environmental loading in the Gulf of Mexico. The input time histories of the force and the moment for the combined model are obtained at the center of gravity of the Spar by using a standard motion analysis program (MLTSIM). The numerical results of the time domain analysis of the combined model, in conjunction with ergodicity, are used for an associated Monte Carlo study. The Monte Carlo study provides useful information regarding the probability densities and the power spectra of various response components of the combined system. These results serve as a benchmark for additional analytical studies that use the technique of statistical linearization to derive equivalent linear stiffness and damping coefficients for the combined system.

Determination of offshore spar stochastic structural response accounting for nonlinear stiffness and radiation damping effects

“…The reliability of the aforementioned simplified model in capturing the predominant features of the system dynamic behavior has been previously established by comparing its responses to specific loads to those of a full-scale detailed model [Spanos et al 2003]. …”

“…Recognizing these limitations of the time domain analysis in capturing the system response statistics, Spanos et al [2005] have suggested a computationally efficient approach for obtaining the spar responses based on a frequency domain representation. In this approach, the nonlinearities of a coupled system consisting of spar, top tensioned risers, and mooring lines are treated by using the concept of statistical linearization.…”

Impacts of top-end vessel sway on vortex-induced vibration of the submarine riser for a floating platform in deep water

“…Generally, the analysis methods concerning interactions of top-end vessel and marine structures can be classified into two kinds: the quasi-static method (Ormberg et al, 1997;Kim et al, 2001;Spanos et al, 2005;Wichers et al, 2001;Xu et al, 2009) and the coupled method (Bosman and Hooker, 1999;Chen et al, 2006;Gu et al, 2012;Li et al, 2010;Tahara and Kim, 2003). In the quasi-static method, riser is simplified as a spring with lumped mass.…”

“…In that case, only the static restoring force, due to wet weight and (or) elastic stiffness of risers, is taken into account. For example, Spanos et al (2005) studied the influence of riser stiffness on the overall dynamic response of a SPAR platform by using a simplified model, in which the top-end vessel mass was concentrated at the gravity center and a horizontal spring was used to simulate the interaction between riser and vessel. Xu et al (2009) (1997), Kim et al (2001) and Wichers et al (2001) investigated the interactions of floating top-end and riser (or mooring system) of deepwater platforms so as to compare the coupled approach in time-domain and the quasi-static approach.…”

Effects of Top-End Vessel Heave on Submarine Riser VIV of Deep Water Platform

“…Generally, the methods of those researches can be classified into two kinds: quasi-static method [8][9][10][11] and coupled method [12][13][14][15][16][17][18] . In quasi-static method, riser is modeled by a spring with lumped mass, and only hydrostatic restoring force of riser is considered.…”