船体上下振動の附加慣性係数におよぼす荷重分布の影響について

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An investigation is made on the effect of load distribution on the virtual inertia coefficient in the vertical vibration of a ship. The virtual inertia coefficient is defined by the ratio of the kinetic energy of the water surrounding the vibrating hull to that of the ship itself as follows; [numerical formula] (1) where, τ_n denotes the virtual inertia coefficient in n-noded flexural vibration of a ship with length L and velocity amplitude y, m_e and m are the two dimensional added mass of water and mass of the ship in unit length respectively, and J_n denotes the longitudinal or three-dimensional correction factor for the n-noded mode flexural vibration of the ship as well-known coefficient obtained by Lewis and Taylor. There are two special cases in the expression of the inertia coefficient, namely, the one in which distributive function of m_e equals to that of m, and the other there is a translational oscillation (n=0). In the above two special cases, the expression (1) yields [numerical formula] (2) where, Δ denotes the displacement of the ship. The equation (2) is the well-known Lewis's method. In general cases, however, the distributive function of the added water mass along ship length is not always coincidental with that of the mass of a ship each other, and also the case n=0 is beside the question in the hull vibration. The inertia coefficient, therefore, should generally computed by the formula (1). As was seen in (1), as there is a variation of the velocity amplitude of the vibration of a ship hull along her length, the distribution of the ship load conspicuously influences the inertia coefficient as well as that on the number of nodes of the ship hull vibration. In the present paper, some numerical calculations following the formula (1) and using a strip method are carried out and the inertia coefficients in some cases are illustrated by the use of the results of experiments on a model ship of modern cargo boat. For obtaining the velocity amplitude of the vertical vibration, the natural modes of vertical vibrations of the model ship in various loading conditions are measured. Besides, to understand the tendency of the increase or decrease of the inertia coefficient for various loading conditions of the ship, the coefficients are obtained analytically evaluating the energies where the m_e- and m-curve are assumed as that of ship form including each different parameters, and the velocity amplitude is assumed to be of the cosine curve with a parameter determined by the minimum energy principle. As a result, the following conclusions have been drawn. (1) The virtual inertia coefficient in the two node vertical vibration of a ship hull which was computed in the present investigation is considerably smaller than that obtained by the Lewis's method, for in the former, the velocity amplitude of the nodal vibration of the ship is taken into consideration. (2) Of the two extreme loading conditions, in the former the load is concentrated near the two nodal points while in the latter the same load is concentrated near the loop and free ends of the mode of the hull vibration in the same draught of a ship. These facts prove that while the inertia coefficient in the first condition is considerably large, that in the second is small. (3) In the normal loading condition, the inertia coefficient is the smallest in the two node or three node vertical vibration, which increases in the higher mode of vibration. It is to be noted, however, that the three-dimensional correction factor generally decreases with the increase of the number of nodes of vibration of a beam in water.
社団法人日本船舶海洋工学会の論文
1962-09-20

船体上下振動の附加慣性係数におよぼす荷重分布の影響について

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