A Unified Ritz Algorithm for Two-Dimensional Sloshing Mode

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Journal of Vibration and Shock ›› 2014, Vol. 33 ›› Issue (19) : 81-85.

论文

A Unified Ritz Algorithm for Two-Dimensional Sloshing Mode

LI Yu-chun, ZHANG Hao

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Abstract

Based on the linear potential theory, the eigenvalue equation of two-dimensional fluid sloshing is derived in this paper. For an arbitrary-shape two-dimensional tank, a unified Ritz algorithm is developed to solve the eigenvalue problem by introducing the Green's first identity and using the base functions of rectangular-section fluid. It avoids a difficulty that a different base function is needed for the various shape tank due to the different boundary condition. The unified Ritz algorithm is suitable for finding the sloshing modes of fluid in the arbitrary-section tanks. The present method is respectively applied to find the sloshing frequencies of the liquids in the canal with 45˚-walls and semi-ellipse tanks. The results of this study agree well with the values by the other analytical methods. The computational accuracy of this algorithm meets the engineering demands.