Proceedings of OMAE 2004 23 rd International Conference on Offshore Mechanics and Arctic Engineering Vancouver, Canada, 20-25 June 2004 OMAE2004-51131 COUPLED NONLINEAR BARGE MOTIONS: PART II: DETERMINISTIC MODELS STOCHASTIC MODELS AND STABILITY ANALYSIS Solomon C. Yim Ocean engineering Program Oregon State University Corvallis, OR 97331, USA Tongchate Nakhata Ocean engineering Program Oregon State University Corvallis, OR 97331, USA Erick T. Huang 1100 23 rd Avenue Naval Facilities Engineering Service Center Port Hueneme, CA 93043-4370 ABSTRACT A computationally efficient quasi-two-degree-of-freedom (Q2DOF) stochastic model and a stability analysis of barges in random seas are presented in this paper. Based on the deterministic 2DOF coupled Roll-Heave model with high- degree polynomial approximation of restoring forces and moments developed in Part I, an attempt is made to further reduce the DOF of the model for efficient stochastic stability analysis by decoupling the heave effects on roll motion, resulting in a one-degree-of-freedom (1DOF) roll-only model. Using the Markov assumption, stochastic differential equations governing the evolution of probability densities of roll-heave and roll responses for the two low-DOF models are derived via the Fokker-Planck formulation. Numerical results of roll responses for the 2DOF and 1DOF models, using direct simulation in the time domain and the path integral solution technique in the probability domain, are compared to determine the effects of neglecting the influence of heave on roll motion and assess the relative computational efforts required. It is observed that the 1DOF model is computationally very efficient and the 2DOF model response predictions are quite accurate. However, the nonlinear roll-heave coupling is found to be significant and needs to be directly taken into account rendering the 1DOF roll-only model inadequate for practical use. The 2DOF model is impractical for long-duration real time response computation due to the insurmountable computational effort required. By taking advantage of the observed strong correlation between measured heave and wave elevation in the experimental results, an accurate and efficient Q2DOF model is developed by expressing the heave response in the 2DOF model as a function of wave elevation, thus reducing the effective DOF to unity. This Q2DOF model is essential as it reduces the computational effort by a factor of 10 -5 compared to that of the 2DOF model, thus making practical stochastic analysis possible. A stochastic stability analysis of the barge under operational and survival sea states specified by the US Navy is presented using the Q2DOF model based on first passage time formulation. INTRODUCTION The stability of ship-to-shore cargo barges under various sea conditions is important to design engineers, especially those of the US Navy. As discussed in Part I, while a barge in general experiences multidirectional sea conditions in the ocean, one of the most critical scenarios leading to capsizing is beam sea. A significant number of researchers have examined the roll stability of ships in beam seas from a stochastic perspective [1-7]. Robert [1, 2] analyzed the roll motion of a ship using the Fokker-Planck (FP) formulation to obtain the probability distribution of the response. Robert et al [3] proposed an averaging approximation to reduce the order of the FP equations from two to one to reduce the computational effort. Dahle et al [4] developed a simple probabilistic model and computed the probability of capsizing under specified sea states. Lin and Yim [5] modeled the roll motion of a ship by the FP equation and studied the effects of noise on Copyright © 2004 by ASME 1