液面晃荡频率的半解析方法

Semi-analytical method for solving liquid surface sloshing frequencies

为了解决内部充液圆柱壳的结构稳定性及安全性会受到内部液体晃荡的影响,本文针对二维圆柱壳在任意充液深度时的自由液面晃荡频率提出了一种半解析求解方法。分别在圆柱壳圆心和自由液面建立结构坐标系和液面坐标系,假设内部液体为无粘不可压缩流体,利用拉普拉斯方程,结合小幅晃荡的表面波方程,得出自由液面的速度势函数,通过坐标变换并结合流体-壳体连续边界条件得出液面运动控制方程,采用伽辽金法得出自由液面晃荡频率。通过与其他方法进行对比验证了晃荡频率及模态求解的准确性,然后对不同充液深度下二维刚性圆柱壳自由液面晃荡频率特性进行了讨论。研究表明:本文提出的方法能够准确有效计算二维充液圆柱壳内部液体不同深度下的晃荡频率。

The structural stability and safety of a liquid-filled cylindrical shell are affected by internal liquid sloshing.Therefore,the sloshing frequency of the internal liquid needs to be studied.In this paper,a semi-analytical method is proposed for the free liquid surface sloshing frequency of a two-dimensional cylindrical shell at any fluid-filled depth.The structure coordinate system and the liquid surface coordinate system are established at the center of the cylindrical shell and the free liquid surface,respectively.The internal liquid is considered an inviscid and incompressible fluid.The fluid velocity potential function is derived by applying the Laplace equation and surface wave equation with small-amplitude sloshing.Then,the Galerkin method is applied to obtain the free liquid surface sloshing frequency.The accuracy of the results is verified by comparing the sloshing frequency and modal solution with published literature and the finite element method.Afterward,the sloshing frequency characteristics of the free liquid surface of a two-dimensional rigid cylindrical shell under different filling depths are discussed.The proposed method could be applied to study free liquid surface sloshing in a liquid-filled cylindrical shell.