Mathematical modeling of the nonlinear roll motion of ships is one subject widely dealt with in nonlinear ship dynamics. This paper investigates setting up a form of nonlinear roll motion model and developing its periodic solution by the generalized Krylov-Bogoliubov asymptotic method in the time domain. In this model, nonlinearities are introduced through damping and restoring terms. The restoring term is approximated as a third-order odd polynomial whereas the quadratic term is favored to represent the nonlinear damping. The ship is assumed to be under the influence of a sinusoidal exciting force. Although the method is expressible to contain any order of the perturbing term, a single degree is chosen to avoid cumbersome mathematical complexity. In order to improve the solution a first-order correction term is also included. Moreover, a numerical example is carried out for a small vessel in order to validate the solution scheme.
Solution of the nonlinear roll model by a generalized asymptotic method
Lösung der nichtlinearen Gleichung für die Rollbewegung von Schiffen mit einem verallgemeinerten asymptotischen Verfahren
Ocean Engineering ; 26 , 11 ; 1169-1181
1999
13 Seiten, 2 Bilder, 2 Tabellen, 5 Quellen
Article (Journal)
English
Generalized Harmonic Analysis of Nonlinear Ship Roll Dynamics
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