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 terms 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. / Graduation date: 2003

Recent developments in estimation of the survivability of a U.S. Navy transport barge in random seas are extended to improve accuracy. The single Degree-of-Freedom (DOF) model of a extreme roll response of a barge used in previous research is replaced by a 3-DOF roll-heave-sway model to include linear and nonlinear static and kinematic coupling between roll, sway and heave. The predominant nonlinearity in the model arises in an improved approximation of the roll righting moment and heave buoyant restoring force by coupling roll with heave. Kinematic coupling is introduced by allowing extreme displacements and rotations in the barge response. System coefficients in the 3-DOF roll-heave-sway model and a simpler 2-DOF roll-heave model are identified by comparing time domain simulations with measured physical model tests of barge motions. Predictions of the 3-DOF and 2-DOF models are compared to measured test data for the case of random waves. Monte Carlo simulations of the equations of motions are performed to predict the reliability of the barge in an operational sea state for a specified mission duration. Use of parallel computer processing is found to make this a viable option for stability estimations as we move into the next century. The stochastic nature of the ocean waves are modeled via filtered white noise. Estimations of the joint probability of the barge responses are presented after application of density estimation kernels. Both the 3-DOF roll-heave-sway model and 2-DOF roll-heave model are tested and compared. Last, examples are provided of some observed nonlinear behavior of the barge motions for variation in damping or ocean wave amplitude. Transient and intermittent chaotic responses are observed for deterministic input waves and quasiperiodic cases are illustrated. / Graduation date: 1996