Investigation of the nonlinear moment influence on the parametric rolling of a ship

Authors: V.Yu. Semenova, D.A. Albaev

 

Abstract

 

The article discusses the definition of parametric roll charatecristics based on the formula of V.V. Lugovskiy. An additional non-linear moment MX is taken into account. Mathematical formulation of the problem has been given, together with its solution. Test calculations of parametric roll for five ships of different types: passenger ship, oil tanker, container ship, timber carrier and bulk carrier — have been given. Roll calculations have been performed at heading angles of 60°, 90° and 120°. RAOs for ships have been calculated with and without non-linear moment consideration. The calculations have been carried out for a given static stability diagram with frequency graphs built based on the Vlasov method. A significant influence of non-linear moment on the maximum amplitudes of parametric rolling have shown, especially for the ship positioned in beam waves, thus demonstrating the need to take the non-linear moment.

 

Keywords: parametric resonance, nonlinear moment, frequency graph, static stability diagram, heave.

 

References

1.   Bogolyubov N.N., Krylov N.M. Vvedenie v nelineynuyu mekhaniku [Introduction into non-linear mechanics] //Izd-vo AN USSR, Kiev. — 1937.

2.   Lugovskiy V.V. Kachka korablya [Ship motions] SPb, 1999.

3.   Lugovskiy V.V. Matematicheskie modeli dlya issledovaniya ustoychivosti nelineynoy kachki sudov na volnenii [Mathematical models to describe the stability of non-linear ship motions in waves] Publ. of International Ship Hydrodynamics Symposium, SPb, 1995, pp. 83 — 91.

4.   Lugovskiy V.V Nekotorye voprosy nelineynoy teorii kachki, svyazannye s obespecheniem ostoychivosti sudna na volnenii [Some aspects of non-linear ship motions theory related to ship stability], SPBGMTU 2008, pp. 93 — 114.

5.   Lugovskiy V.V. Nelineynye zadachi morekhodnosti korablya [Aspects of non-linear ship motions], L., Sudostroenie, 1966.

6.   Lugovskiy V.V. Teoriya i priblizhenny raschet bortovoy kachki sudna s zadannoy diagrammoy ostoychivosti na kosykh uglakh po otnosheniyu k volneniyu [Theory and approximate calculations of ship roll motions with given stability diagram for quartering seas] // NTO Sudproma. Collection of articles No. 39. L., 1961, pp. 117 — 136.

7.   Spravochnikpo teorii korablya [Ship theory reference book], Vol. 2. / (ed. Ya.I. Voytkunsky) L., Sudostroenie, 1985.

 

About authors:

 

V.Yu. Semenova - DSc, professor, St. Petersburg State Marine Technical University, St. Petersburg, e-mail: sem_viktoria@mail.ru

D.A. Albaev - St. Petersburg State Marine Technical University, St. Petersburg, e-mail: albaevdanil@gmail.com

Issue: 66/67 (2022)

For citation: V.Yu. Semenova, D.A. Albaev. Investigation of the nonlinear moment influence on the parametric rolling of a ship. Research Bulletin by Russian Maritime Register of Shipping. 2022, No. 66/67, pp. 30-38.

UDC 629.12.073.243.4

Pp: 30-38