Unusual roll motion modes of an unstable ship in waves

Author: S.G. Zhivitsa

Abstract

The mathematical model reflecting quantitatively and qualitatively all the principle features of an unstable ship rolling in waves is proposed in the article. It has been shown that an unstable ship's roll motion differs from the rolling of a ship with positive initial metacentric height. Using the analytical varied scale method of roll equation's analysis the specific oscillation regimes for an unstable ship have are proposed: depending on frequency and intensity of waves the unstable ship rolls either with small amplitudes around stable equilibrium position or with large amplitudes around unstable upright equilibrium position. Transiting between the above rolling regimes with small and large amplitudes the ship can be drawn in chaotic roll motion. It has been determined that in sea voyage an unstable ship can undergo resonance roll motions in wide frequency range: in the case of coincidence of the incoming wave frequency and a ship roll natural frequency principle resonance occurs; in the case of the incoming wave frequency two times exceeding the natural roll frequency either sub-harmonic resonance of the second kind or parametric resonance occur; if the wave frequency is three times higher than natural roll one the sub-harmonic resonance of the third kind may be observed. Analytical expressions are proposed to determine the maximum roll amplitudes of the ship with negative initial stability for the cases of roll motions in all the above indicated resonance modes, as well as the conditions of their excitation.

Keywords: unstable ship, roll motions in waves, principal resonance, parametric resonance, sub-harmonic resonance, chaotic motions

References

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2. Wang Y.G. Melnikov Analysis of a Ship's Stability with Water-on-Deck. Journal of Marine Science and Technology, 2010, vol. 18, no. 1, pp. 106 - 111.

3. Bondar N.G. Nelineinye stacionarnye kolebaniya [Nonlinear stationary oscillations]. Kiev, Naukova dumka, 1974, 211 p.

About author

S.G. Zhivitsa - PhD, Krylov State Research Centre, St. Petersburg, e-mail: 9_otd@ksrc.ru

For citation: S.G. Zhivitsa. Unusual roll motion modes of an unstable ship in waves. Research Bulletin by Russian Maritime Register of Shipping. 2018, No. 52/53, pp. 28-34.

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UDC:  629.12.073
Pages:  28-34