There is a paper on it [Reference: Grim. O "Die Schwingungen Von Schwimmender Zweidimensionalen", korpern, HSVA, Report 171,1959] but sorry to say that is in 'German language'.
It will be nice of you if you help me to find another article or theoretical source.
(Thanks)
Dear Mohammed,
maybe it would help to make your question a bit more specific. The plots seems to refer to solution using conformal mapping.
Please mention the reference (in English) from which you took the figure and the short part of the text defining the amplitude ratio.
For some classical references you can take a look at these:
Lewis, F.M., 1929. The inertia of the water surrounding a vibrating ship, in: 37th Meeting of The Society of Naval Architects and Marine Engineers, SNAME.
Ursell, B.F., 1949. On the heaving motion of a circular cylinder. Q. J. Mech. Appl. Math. II, 218–231.
Frank, W., 1967. Oscillation of cylinders in or below the free surface of deep fluids. Naval Ship Research and Development Center, Washington
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