Abstract
This paper investigates mathematical modelling of response amplitude operator (RAO) or transfer function using the frequency-based analysis for uncoupled roll motion of a floating body under the influence of small amplitude regular waves. The hydrodynamic coefficients are computed using strip theory formulation by integrating over the length of the floating body. Considering sinusoidal wave with frequency (ω) varying between 0.3 rad/s and 1.2 rad/s acts on beam to the floating body for zero forward speed, analytical expressions of RAO in frequency domain is obtained. Using the normalization procedure and frequency based analysis, group based classifications are obtained and accordingly governing equations are formulated for each case. After applying the fourth order Runge-Kutta method numerical solutions are obtained and relative importance of the hydrodynamic coefficients is analyzed. To illustrate the roll amplitude effects numerical experiments have been carried out for a Panamax container ship under the action of sinusoidal wave with a fixed wave height. The effect of viscous damping on RAO is evaluated and the model is validated using convergence, consistency and stability analysis. This modelling approach could be useful to model floating body dynamics for higher degrees of freedom and to validate the result.
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Foundation item: The financial grant of Islamic Azad University Kermanshah branch, Iran (Grant No: 35/3/622281, 7-9-2009)
Samir K. Das is Professor and Head in the Department of Applied Mathematics, Defence Institute of Advanced Technology. Prof. Das has obtained his Ph.D from Indian Institute of Technology (IIT) — Kharagpur in the year 1987. He has completed 24 client-sponsored engineering project of national and international importance that includes World Bank sponsored project as well. His research focus and area of interest are theoretical, computational and environmental fluid dynamics, mathematical modelling of engineering problems and floating body motion in waves. He has already supervised several PhD students and guided nearly 50 Masters thesis (M.Sc/M.C.A/M.Tech). He has published 75 research papers in various journals and conferences that also include 5 contributed article in books. He is a reviewer of several national and international journals of repute and also in the Editorial Board of 10 national/international journals. He has delivered invited/guest lectures at various national and international conferences and symposiums in India and abroad.
Masoud Baghfalaki is currently Head of the Department of Mathematics, Payame Noor University of Kermanshah, Kermanshah branch, Kermanshah, Iran. Earlier, he was a faculty of Islamic Azad University, Kermanshah branch, Kermanshah, Iran. He has also worked for various academic and administrative positions. He has submitted his Ph.D thesis, University of Pune, India. He has published five research papers and communicated few more papers in the international journals.
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Das, S.K., Baghfalaki, M. Mathematical modelling of response amplitude operator for roll motion of a floating body: Analysis in frequency domain with numerical validation. J. Marine. Sci. Appl. 13, 143–157 (2014). https://doi.org/10.1007/s11804-014-1249-7
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DOI: https://doi.org/10.1007/s11804-014-1249-7