流力弾性問題における相似則 : 第1報,相似則の導出

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As ocean going vessels and floating offshore structures with huge size and with various shape have been so developed as to meet the highly advanced demands in the sea, their experimental validation has been placed a higher value on for the purpose of rational design. In some cases, the use of an elastic scale model is indispensable because the interaction between its structural rigidity and hydrodynamic effects plays a significant role. The main concern of the paper is to derive fundamental laws of similitude which regulate the hydro-elasticity problems. An equation of torsional vibration has been developed by modifying Timoshenko equation which was derived for a rectangular plate model by Kumai. The laws have been derived through analyses of free vibration for vertical bending and torsion. The characteristics of floating structures have been represented, assuming the similarity in the fluid action on the basis of Froude number, in terms of six non-dimensional parameters in which vertical bending rigidity, tor-sional rigidity and shear rigidity are included as the representative of structural elastic properties. The laws which precisely realize the similitude for all the parameters, under the assumption that the geometrical similarity is perfectly retained not only in overall configuration but also in detail members, are found to be unified to a single equation which describes the relation between the supporting fluid and the elastic modulus. Though the law is simple, its realization is quite difficult. The actual alternative to that is to hold the similitude only in dominant parameters disregarding other minor ones. The contribution of all the parameters has been evaluated through sensitivity analyses of natural frequencies. That leads to the conclusions. In the case of huge shallow structures : 1) The similitude on static restoring effects goes first in the range of lower order vibration mode, but the role of the elastic properties grows in the higher order range. In the case of rigid structures like ship hulls : 2) The priority of the similitude should be placed first on the bending rigidity and second on the shear rigidity for vertical bending, and first on the shear rigidity and second on the torsional rigidity for torsional action. 3) The contribution of the similitude on shear rigidity should be emphasized especially when their higher order vibrations are concerned.

流力弾性問題における相似則 : 第1報,相似則の導出

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