Access Type

Open Access Dissertation

Date of Award

January 2011

Degree Type


Degree Name



Mechanical Engineering

First Advisor

Raouf A. Ibrahim


This study deals with impact interaction of ships with one-sided ice barrier during roll dynamics. An analytical model of ship roll motion interacting with ice is developed based on Zhuravlev and Ivanov non-smooth coordinate transformations. These transformations have the advantage of converting the vibro-impact oscillator into an oscillator without barriers such that the corresponding equation of motion does not contain any impact term. Such approaches, however, account for the energy loss at impact times in different ways. The present work, in particular, brings to the attention the fact that the impact dynamics may have qualitatively different response characteristics to different dissipation models. The difference between localized and distributed equivalent damping approaches is discussed. Extensive numerical simulations are carried out for all initial conditions covered by the ship grazing orbit for different values of excitation amplitude and frequency of external wave roll moment. The basins of attraction of safe operation are obtained and reveal the coexistence of different response regimes such as nonimpact periodic oscillations, modulation impact motion, period added impact oscillations, chaotic impact motion and rollover dynamics.

An experimental investigation conducted on a small ship model. In particular, the experimental tests reveal complex dynamic response on multi-frequency wave motion caused by the wave reflection from the tank walls. Measured results showed a good agreement with the predicted results for small angles of the barrier relative to the ship unbiased position. However, deviation becomes significant as the angle increases. This deviation is mainly attributed to the uncertainty of the coefficient of restitution, which is found to depend on the velocity of impact in addition to the geometry and material properties of the model and barrier.