Stability analysis of nonlinear coupled barge motions

The present research investigates nonlinear barge motions through analyses of coupled multi-degree-of-freedom (MDOF) deterministic and stochastic models. Roll-Heave-Sway and other lower-ordered models are developed to predict the nonlinear motions and analyze the stability of a class of ship-to-shore cargo barges. The governing equations of motion contain coupled rigid body Roll-Heave-Sway relations, hydrostatic and hydrodynamic terms. The rigid body relationships are a part of the general six-degree-of-freedom model. Hydrostatic terms include effects of the barge's sharp edge and of relative Roll-Heave states. Hydrodynamic terns are in a “Morison” form. The characteristics of the excitation wave field are based on linear wave theory.; Predictive capabilities of the Roll-Heave-Sway and the Roll-Heave models are investigated. System parameters are calibrated to match experimental test results using several regular wave test cases. Potential theory predictions provide initial estimates of several key system parameters. With the identified system parameters, numerical predictions obtained from time domain simulations of both models are compared with experimental test results for a random wave case, and compared to each other to investigate the coupling effects of sway on roll and heave motions.; Reliability against capsizing of a barge in random seas is investigated using stochastic analysis techniques. With the Markov process assumption, the barge response density to random waves is derived as a solution to the corresponding Fokker-Planck equation. The path integral solution technique is employed to obtain numerical solutions for the Roll-Heave and the Roll models. A quasi-2DOF model is introduced to improve the accuracy of the 1DOF Roll model. The reliability of a barge in a variety of sea conditions is analyzed as a first passage problem using the quasi-2DOF model. Mean times to reach specified capsizing probabilities for a barge operating in sea states 1 through 9 are obtained.