NONLINEAR DYNAMICS

Planing Dynamics. Unlike displacement hulls, the dynamics of planing craft generally do not lend themselves to linear analysis. The high speeds, small trim angles, and shallow drafts of such vessels produce large changes in wetted surface which, in turn, lead to significant hydrodynamic and dynamic nonlinearities. Due to the complex nonlinearities of this type of craft, naval architects and planing boat designers tend to rely upon experimental tests or simulation for guidance. In order for simulation to be an effective design tool, a fundamental understanding of the system's dynamic characteristics is required. Model reduction coupled with path following or continuation methods allow for the identification of various types of system behavior which include dynamic instabilities such as propoising and chine walking. With the ability to avoid these undesirable motions, a safe and efficient planing hull design is possible.

Capsizing. This area of research has combined geometric methods for nonlinear systems with simulation. Analytical results provide a measure of the rate of phase space transport, but are also directly related to capsize. The methodology demonstrates a probabilistic approach applicable to safety of ships at sea and thus provides a measure of initiation of capsize in that environment.

Comparison of capsize prediction methods using phase flux theory and simulation. Probability of capsize is based upon simulation. Theoretical onset of capsize is based upon the asymptote of phase flux (ref. Hsieh, Troesch, and Shaw, 1994).

Ice Structure Interaction. Contact dynamics are fundamentally nonlinear due to the abrupt change in stiffness when contact is made or lost. A system comprised of a mechanical oscillator subjected to intermittent contact with a series of elastic-brittle teeth models the process of an ice sheet impinging against an elastic offshore structure. Nonlinear systems analysis is used to study and predict the various types of behavior, some of which could have disastrous consequences.

Poincaré section for a model of an imperfect ice-structure system with random ice sheet parameters. The displacement (x) represents a characteristic degree of freedom of the structure (ref. Karr, Troesch, and Levi, 1995).

Towing System Dynamics. Nonlinear dynamics and bifurcation theory have been used to develop a design methodology for systems that eliminate trial and error and lengthy simulations. For more details, refer to Spread Mooring System Dynamics in the Offshore Mechanics research focus area.

FACULTY: Bernitsas, Karr, Troesch