二维晃动模态的统一Ritz计算格式

PDF(1219 KB)

振动与冲击 ›› 2014, Vol. 33 ›› Issue (19) : 81-85.

论文

二维晃动模态的统一Ritz计算格式

李遇春，张皓

作者信息 +

A Unified Ritz Algorithm for Two-Dimensional Sloshing Mode

LI Yu-chun, ZHANG Hao

Author information +

文章历史 +

摘要

基于线性势流理论，本文推导了液体二维晃动的特征值方程，对于任意二维容器，通过引入第一Green公式，将矩形截面晃动模态的精确解作为基函数，提出了特征值问题Ritz统一计算格式，避免不同截面(不同的边界条件)需要引入不同基函数的复杂性，使得Ritz方法适用于任意截面内液体的二维晃动模态分析，可同时求解晃动频率与振型。本文方法分别用于求解半顶角为45˚的三角形渠道、半椭圆形截面内液体的晃动频率，本文计算结果与其它解析方法的结果吻合良好，其计算精度完全满足工程要求。

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.