|M.Sc Student||Kleiman Alexander|
|Subject||Nonlinear Dynamics and Parametric Instabilities of Ships|
Subject to Head Seas
|Department||Department of Mechanical Engineering||Supervisor||Professor Oded Gottlieb|
|Full Thesis text|
Finite amplitude dynamics leading to capsize of ships in head seas due to parametric instabilities is a subject of renewed interest with the increasing demand of operation in severe and variable environmental conditions. Current investigations have focused on small scale experimental response in towing tanks and numerical integration of various simulators ranging from simple single-degree-of freedom models to fully coupled rigid-body dynamics that require predetermined hydrodynamic coefficients describing the system restoring force, added mass and damping characteristics. However, comparison of experimental and numerical results reveals discrepancies which prevent accurate representation of ship dynamics leading to capsize. These discrepancies include simplistic decoupled modeling that is unable to predict finite angle response where equal pitch and heave natural frequencies are nearly double that of the roll. This reflects the extreme conditions for the heave - pitch - roll internal resonance (2:2:1), where equivalent linearization or construction of standard nonlinear parametrically excited roll models are unable to predict coupled large amplitude response leading to capsize. Thus, in order to resolve the inaccuracies and instabilities associated with the coupled wave-structure interaction system, we derive, validate, and analyze a dynamical system for roll-pitch-heave dynamics that consistently couples all system nonlinearities. The research benefits from an analytical approach including asymptotic and global solutions, complemented by numerical integration of the nonlinear dynamical system. This combined approach is original and resolves both internal resonances and parametric instabilities induced in both weak and finite nonlinear interaction, culminating with approximate analytical local and global orbital stability thresholds.