液体貯槽における有限振幅液面動揺に関する研究 : (その1)基礎方程式の誘導とその円筒形貯槽への適用

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タイトル別名
  • ON THE SLOSHING WITH FINITE AMPLITUDE IN THE LIQUID STORAGES
  • 液体貯槽における有限振幅液面動揺に関する研究-1-基礎方程式の誘導とその円筒形貯槽への適用
  • エキタイ チョソウ ニ オケル ユウゲン シンプク エキメン ドウヨウ ニ カ

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According to the ordinary linear potential flow theory, natural frequencies of the containing liquid and linear responses of the storage except those on the neighborhood of the resonance frequencies can be obtained with relatively good accuracy. There is however possibility that the containing liquid is enforced to oscillate with the frequencies in the neighborhood of the resonance points resulting in large amplitude liquid motion, as frequently mentioned in the recent disaster reports. Under these circumstances, the effect of nonlinearity due to finite free surface elevation comes to be necessary to be taken into account for the correct analysis of the behavior of the containing liquid as well as the responses of the storage. In this paper, a numerical method for solving the nonlinear sloshing problem of the inner liquids of cylindrical rigid storage is presented. The variational principle is adopted to formulate the governing nonlinear equation interms of the unknown velocity potential and response free surface elevation by means of the Taylor series expansion of the unknown variables about the undisturbed free surface. In order to obtain the oscillative characteristics over a wide range of sloshing frequencies the stationary oscillative analysis based on a harmonic balance technique is presented. From the results of the numerical calculations, possibilities of existence of some nonlinear resonance responses in the neighborhood of the first resonance frequency are shown as well as the bi-harmonic responses of the spatial mode with the circumferential wave number n=0 or 2.

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