研究二维矩形月池流体的自振特性。基于线性势流理论，采用 Galerkin 展开，将问题转化为月池自振频率特征值问题，求解自振频率及速度势函数的系数矩阵，获得二维矩形月池固有频率及振型的半解析解，分析月池几何参数对月池流体自振特性影响。研究表明，由于内部与外流连通，月池流体呈垂向活塞（piston）振动及晃荡（sloshing）运动两种形式。垂向活塞振动模态频率变化主要受液面高度影响，且随液面高度增加而减小；晃荡模态频率主要受月池宽度影响，随月池宽度增加而减小。活塞振动模态振型在液面较浅时出现波峰，随液面高度增加而消失。利用 CFD 方法计算月池运动，结果与半解析解中振型曲线拟合良好。%Based on the linear potential theory,the equations of fluid motions in a two dimensional rectangular moonpool were converted into an eigenvalue problem by Galerkin method.Via solving the coefficient matrix of potential function,the semi-analytical solution of natural frequencies and shapes of fluid was obtained and the influences of geometric parameters of the moonpool on its natural vibration characteristics were discussed.The results show that there exist two natural vibration modes of fluid in the moonpool,namelt,the piston mode and sloshing mode.The piston mode frequency in vertical direction decreases as the liquid height increases and is mainly determined by the liquid height, whereas sloshing mode frequencies decreases as the moonpool width increases and mainly depend on the moonpool width. In the piston mode shape crest appears as the liquid depth is small,and vanishes as the liquid depth increases.The CFD method was used to verify the semi-analytical solution and the free surface curves in the two results are in good coincidence.
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