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 Samir K. Das Masoud Baghfalaki.Mathematical Modelling of Response Amplitude Operator forRoll Motion of a Floating Body: Analysis inFrequency Domain with Numerical Validation[J].Journal of Marine Science and Application,2014,(2):143-157.[doi:10.1007/s11804-014-1249-7]
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Mathematical Modelling of Response Amplitude Operator for Roll Motion of a Floating Body: Analysis in Frequency Domain with Numerical Validation


Mathematical Modelling of Response Amplitude Operator for Roll Motion of a Floating Body: Analysis in Frequency Domain with Numerical Validation
Samir K. Das Masoud Baghfalaki
Samir K. Das Masoud Baghfalaki
1. Department of Applied Mathematics, Defence Institute of Advanced Technology, Girinagar, Pune-411025, India 2. Department of Mathematics, Islamic Azad University, Kermanshah branch, Iran
RAO roll motion hydrodynamic coefficient Froude-Krylov force added mass damping floating body frequency domain
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 ( ) 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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The financial grant of Islamic Azad University Kermanshah branch, Iran (Grant No: 35/3/622281, 7-9-2009)
Last Update: 2014-06-10