矩形水槽壁の接水振動について(第4報)

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When side-walls of a rectangular tank, which is filled up with water, is vibrating, the inside water will also make a vibratory motion. Accordingly, the value of natural frequency of vibration of side-wall will be considerably lowered, due to presence of water. This effect is represented by "virtual mass" of water.The author have reported, in previous papers of the same title, some results of theoretical study about the "virtual mass" of water. In these studies, two conditions at the top-surface of water were considered, namely ; (a) the top of water is directly in contact with a rigid plane wall.(b) the top of water is left free, forming a state of "free surface".As to the case (b), an approximate formula for the "virtual mass" of water was obtained, by assuming that value of the factor K=ω^2H/g (wherein ω=angular frequency of vibration, H=depth of the tank, g=accerelation due to gravitation of the earth), is very large in comparison with unity. It is thought that this assumption is appropriate, at least in the case of vibration of side-walls constituting the water- or oil-tank in a ship.But, there may arise the questions (a) what degree of approximation it will give? (b) what will take place, if the factor K was not so large in comparison with unity? In the present report, these questions are studied, theoretically. As before, the water is assumed to be an incompressible ideal fluid, and the vibration to be of infinitesimally small amplitude. It is shown, by taking up the numerical example for the case of a rectangular water tank having the proportion of H : B : L=3 : 3 : 5,that, if the value of coefficient K is as large as 1000,the author's approximate formula (given in Report I), is sufficiently accurate for a practical use, but that if the value of K is as low as 10,it requires considerable modification.
社団法人日本船舶海洋工学会の論文

矩形水槽壁の接水振動について(第4報)

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