Inelastic impact dynamics of ships with one-sided barriers. Part I: analytical and numerical investigations |
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Authors: | Ihab M Grace Raouf A Ibrahim Valery N Pilipchuk |
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Institution: | 1.Department of Mechanical Engineering,Wayne State University,Detroit,USA |
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Abstract: | This two-part paper deals with impact interaction of ships with one-sided ice barrier during roll dynamics. The first part
presents analytical and numerical studies for the case of inelastic impact. An analytical model of a 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, demonstrates 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 non-impact periodic oscillations, modulation impact
motion, period added impact oscillations, chaotic impact motion and rotational motion. The second part will consider experimental
validations of predicted results. |
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Keywords: | |
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