Area of the unstable solution of rolling equation : jumps of the oscillations amplitude

• Autorzy: Wawrzyński W.

Identyfikatory

DOI

10.5604/01.3001.0012.4372

• Języki publikacji: EN

Abstrakty

EN

The most interesting motion of the ship is rolling. This is because the rolling amplitudes are much bigger than amplitudes of other degrees of freedom and under resonance conditions, which can exceed 40º. In such a case, when the maximum of the righting arm curve is placed at relatively small angles, the roll equation reveals a strongly nonlinear character and bistability areas as well as an area of unstable solutions of the roll equation occurs. Together with the appearance of the above-mentioned areas, amplitude jumps are possible. In the study, the case of strongly nonlinear rolling is analysed. For the purpose of numerical simulations, the 1DOF mathematical model of rolling with damping dependent on amplitude and frequency is used. The article presents the roll spectrum including the bistability areas and the area of unstable solutions for one loading condition of the offshore support vessel. It is demonstrated that for strongly nonlinear rolling, rolling with two different amplitudes for the same value of excitation is possible. It is also shown that transitions (jumps) between these amplitudes are possible too. A few scenarios of jumps of the rolling amplitude within the region of unstable solutions of the rolling equation are presented. The presented rolling scenarios show that under some circumstances rolling can be observed as chaotic.

Słowa kluczowe

EN

ship rolling; nonlinear oscillations; nonlinear resonance; bistability; bifurcations; amplitude jumps

• Wydawca: Łukasiewicz Research Network - Institute of Aviation ; European Science Society of Powertrain and Transport KONES Poland ; Wydawnictwo Instytutu Technicznego Wojsk Lotniczych
• Czasopismo: Journal of KONES
• Rocznik: 2018
• Tom: Vol. 25, No. 3
• Strony: 489--496
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Wawrzyński W.

• Gdynia Maritime University Faculty of Navigation, Department of Ship Operation Jana Pawła II Av. 3, 81-345 Gdynia, Poland tel.: [phone]

Bibliografia

• [1] Bassler, C., Reed, A., A method to model large amplitude ship roll damping, Proceedings of the 11th International Ship Stability Workshop, pp. 217-224, 2010.
• [2] Falzarano, J., Taz Ul Mulk, M., Large amplitude rolling motion of an ocean survey vessel, Marine Technology, Vol. 31, pp. 278-285, 1994.
• [3] Fossen, T., Nijmeijer, H., (eds.), Parametric resonance in dynamical systems, Springer Science Business Media, LLC, http://dx.doi.org/10.1007/978_1-4614_1043-0, 2012.
• [4] Francescutto, A., Contento, G., Bifurcations in ship rolling: experimental results and parameter identification technique, Ocean Eng., Vol. 26, pp. 1095-1123, 1999.
• [5] Himeno, Y., Prediction of ship roll damping – state of the art, Report of Dept. of Naval Architecture and Marine Engineering, The University of Michigan, No. 239, 1981.
• [6] ITTC Recommended Procedures, Numerical Estimation of Roll Damping, ITTC, 2011.
• [7] Jordan, D. W., Smith, P., Nonlinear ordinary differential equations – An introduction for scientists and engineers (4th ed.), Oxford University, 2007.
• [8] Kawahara, Y., Maekawa, K., Ikeda, Y., A simple prediction formula of roll damping of conventional cargo ships on the basis of Ikeda’s method and its limitations, Journal of Shipping and Ocean Engineering, Vol. 2, pp. 201-210, 2012.
• [9] Kiewrel, A., Nieliniowy rezonans mechaniczny w modelach matematycznych maszyny synchronicznej, Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych Politechniki Wrocławskiej, Nr 50, pp. 251-259, 2000.
• [10] Liangqiang, Z., Fangqi, Ch., Stability and bifurcation analysis for a model of a nonlinear coupled pitch–roll ship, Mathematics and Computers in Simulation, Vol. 79, pp. 149-166, 2008.
• [11] Wawrzyński, W., Krata, P., On ship roll resonance frequency, Ocean Eng., Vol. 126, pp. 92-114, 2016.
• [12] Wawrzyński, W., Bistability and accompanying phenomena in the 1-DOF mathematical model of rolling, Ocean Eng., Vol. 147, pp. 565-579, 2018.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).