Unsymmetrical Movements of a Multi-Hull Vessel Treated as a Linear Objects

• Autorzy: Królicka, A.
• Języki publikacji: EN

Abstrakty

EN

Due to difficulties in determining accurate initial conditions for the motion of sea waves and the nature of wind waves, modelIing the dynamics of sea waves can be only done within the framework of the stochastic theory. The floating objects selected for the analysis represent multi-hull objects such as catamarans and trimarans, due to the availability of codes calculating hydrodynamie coefficients and exciting forces generated by regular wave. The examined floating object is treated in the article as a linear dynamie system with 6 freedom degrees. The multi-hull object with a rigid structure sails with a flXed forward speed Vo. The motion of a surface marine floating object id defined by a system of 6 second-order linear differential equations. lf the model of the dynamie system is a linear model of the floating object, then the above system of differential equations can be analysed as a system of two separate groups of mutually coupled equations. Group 1 includes symmetric (longitudinal) movements, while group 2 - antisymmetric (lateral) movements. Group 1 includes: linear longitudinal movements (n1), linear vertical movements (n3) and angular longitudinal movements (n5). This group of movements was discussed in detail in [5]. The present article is a continuation ofthe analysis ofthe dynamics of marine floating objects and refers to group 2 of the equations deseribing lateral movements, which include: lateral linear movements - sway (n2), lateral angu- lar movements - roll (n4), horizontal angular movements - yaw (n6). The article discusses the system of stochastic differential equations for coupled unsymmetrical movements. The coupling is assumed to be executed via linear and nonlinear coefficients of damping and hydrostatic elasticity. The final equation system is presented in vector form using Itó equations. Further analysis of the problem will refer to statistic moments, examined using the theory of Markov processes and the Fokker-Planck-Kolmogorow equation. The method based on the theory of Markov processes in the second-order form with partial derivatives, and making use ofthe Fokker-Planck-Kolmogorow equation for the eon tional probability density function (passing function) can be effectively used in stu ing the dynamics of randomly excited floating objects.

• Czasopismo: Marine Technology Transactions. Technika Morska
• Rocznik: 2007
• Tom: Vol. 18
• Strony: 63-74
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Królicka, A.

• Gdańsk University of technology, Faculty of Ocean Engineering and Ship Technology ul. Narutowicza 11/12, 80-952 Gdańsk, Poland,

Bibliografia

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• 5. Królicka A., Stochastic approach to the dynamics of a linear floating object. Marine Technology Transactions, Vol. 17. pp. 121 130. Gdańsk 2006.
• 6. Rumianowski A., Dynamic tests of selected marine floating objects. Gdańsk 2003 (in Polish).
• 7. Rumianowski A., Stochastic approach to the dynamics of marine floating objects. Marine Technology Transactions. Vol. 17. pp. 155-165, Gdańsk 2006.
• 8. Sobczyk K., Stochastic differential equations. Warszawa 1996 (in Polish).
• 9. Sobczyk K., Spencer Jr., B. F., Stochastic models of material fatigue. Wydawnictwa Naukowo-Techniczne, Warszawa 1996 (in Polish).
• 10. Wu M. K., Moan T., Numerical prediction of wave-induced long-term extreme load effects in a flexible high-speed pentamaran. Journal of Marine Science and Technology, Vol. 11, Number 1, pp. 39-51. 2006.