Publisher DOI: 10.1007/s00773-021-00810-4
Title: Theoretical determination of asymmetric rolling amplitude in irregular beam seas
Language: English
Authors: Maki, Atsuo 
Dostal, Leo 
Maruyama, Yuuki 
Sakai, Masahiro 
Katayama, Toru 
Sugimoto, Kei 
Fukumoto, Yusuke 
Umeda, Naoya 
Keywords: Asymmetricity of roll motion;Energy-based averaging method;Irregular beam seas;Roll amplitude
Issue Date: 2021
Source: Journal of Marine Science and Technology (inPress): (2021)
Journal: Journal of marine science and technology 
Abstract (english): 
A methodology for predicting the probability density function of roll motion for irregular beam seas is developed in the author’s previous research. In this paper, two methods for the prediction of the probability density function (PDF) of the rolling amplitude are examined. One of these methods is an approach based on a non-Gaussian PDF with the use of the equivalent linearization and the moment method, which has been used by Maki in the field of naval architecture. In the framework of this method, the instantaneous joint PDF of the roll and roll rate can be calculated. Thereby, the transformation from the joint PDF to the PDF of the total energy H is necessary. In this paper, the transformation from the joint PDF of instantaneous roll and rate to the PDF of H was conducted. The other method is the energy-based stochastic averaging method, whereby the PDF of the total energy H is determined from which the roll amplitude is calculated. It is noteworthy that the proposed theory aims to predict the PDF of the amplitude of the vessel due to wind or flooding. For such conditions, the restoring curve (GZ curve) has asymmetricity. To take into account this asymmetricity, a new theory for the transform of the PDF of the total energy H to the PDFof amplitude is proposed. The obtained theoretical results show almost complete agreement, and both of the two theoretical methods i.e., the energy-based stochastic averaging method and the non-Gaussian PDF method with the use of the equivalent linearization and moment method, show equivalent prediction performance even in the asymmetric condition.
ISSN: 0948-4280
Institute: Mechanik und Meerestechnik M-13 
Document Type: Article
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