Non-linear damping coefficients from an asymmetric roll decay time series: An analytical method

Spyrou, KJ

dc.contributor.author	Spyrou, KJ	en
dc.date.accessioned	2014-03-01T01:21:08Z
dc.date.available	2014-03-01T01:21:08Z
dc.date.issued	2004	en
dc.identifier.issn	14750902	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16082
dc.subject	Elliptic functions	en
dc.subject	Non-linear	en
dc.subject	Roll damping	en
dc.subject	Roll decay	en
dc.subject	Ship	en
dc.subject	Stability	en
dc.subject.other	Aerodynamics	en
dc.subject.other	Energy dissipation	en
dc.subject.other	Functions	en
dc.subject.other	Probability	en
dc.subject.other	Ships	en
dc.subject.other	Stability	en
dc.subject.other	Wind effects	en
dc.subject.other	Elliptic functions	en
dc.subject.other	Non-linear	en
dc.subject.other	Roll damping	en
dc.subject.other	Roll decay	en
dc.subject.other	Damping	en
dc.title	Non-linear damping coefficients from an asymmetric roll decay time series: An analytical method	en
heal.type	journalArticle	en
heal.identifier.primary	10.1243/147509004774048532	en
heal.identifier.secondary	http://dx.doi.org/10.1243/147509004774048532	en
heal.publicationDate	2004	en
heal.abstract	A method to extract non-linear ship roll damping coefficients from an asymmetric roll decay record is developed by following an analytical route. Customarily, the existence of bias in the roll equation is dealt with either through a constant term in the external forcing or through an asymmetric restoring. With suitable variable transformations and time scaling, the conditions of equivalence between these two representations are established. The main body of the paper begins with the derivation of the law of (asymmetric and non-linear) roll motion decay, initiated from an angle near to the vanishing angle. This involves the following three steps: (a) finding the solution ('orbit') of the corresponding Hamiltonian system, (b) using the velocity along the Hamiltonian orbit for approximating the amount of energy dissipated in a half-cycle of the real system, through exact analytical calculation of a number of elliptic integrals and (c) extracting the decay law by balancing the dissipated energy against the lost potential one. The use of this law for deriving non-linear roll damping coefficients is subsequently described. The applicability of the proposed methodology is demonstrated with an example. © IMechE 2004.	en
heal.journalName	Proceedings of the Institution of Mechanical Engineers Part M: Journal of Engineering for the Maritime Environment	en
dc.identifier.doi	10.1243/147509004774048532	en
dc.identifier.volume	218	en
dc.identifier.issue	1	en
dc.identifier.spage	11	en
dc.identifier.epage	21	en