带隔板的矩形截面渡槽内液体的晃动特性

摘要

The small amplitude sloshing of an ideal fluid in a rectangular rigid aqueduct with a rigid baffle was studied.The complicated fluid domain caused by the baffle was divided into several sub-domains with simple shape and uniform boundary conditions.The velocity potential functions corresponding to each fluid sub-domain were studied.The general expressions for the modal shape functions of sub-domains were analytically deduced by using the method of separation of variables based on the superposition principle.According to the continuous conditions of velocity and pressure at the interface between two sub-domains and the free fluid surface wave conditions,the unknown coefficients in the velocity potential solutions were uniquely obtained.The natural sloshing frequencies and modal functions were numerically determined by using the Fourier series expansion.%研究带有刚性隔板的矩形截面渡槽中液体的微幅线性晃动特性。将因隔板而导致的复杂液体域分割为若干个形状简单且边界条件均一的子域，分别研究各子域内液体运动的势函数。利用叠加原理和分离变量法，导出每个子域内液体速度势的一般解。根据液体子域界面处速度和压力的连续条件以及自由液面处的表面波条件，得到含有待定系数的级数方程。对方程作 Fourier 展开，即可求得液体的固有晃动频率和振型函数。