本文研究了水平激励下二维矩形储箱中流体的晃动，抑制晃动的装置为竖向的刚性隔板，建立了隔板在储箱自由液面处的解析模型。首先通过引入人工界面的方式，将流体域划分成若干个流体子域，使每个流体子域对应的速度势函数满足C1连续性条件。基于叠加原理，使用分离变量法求得每个流体子域的速度势的形式解，将形式解代入子域间界面与自由液面条件可得含有待定系数的级数方程，通过加权积分消去方程中的空间坐标，截断方程可得特征方程，由此可得晃动频率与模态。将水平激励下的速度势函数分解为摄动速度势与刚体速度势，将摄动速度势和刚体速度势代入自由液面的波动方程即可求得含广义坐标的动力响应方程，求解该方程可得储箱中流体的晃动响应。
Abstract
The sloshing of liquid in a 2-D rectangular container under horizontal excitation is investigated. The sloshing control device is a rigid vertical baffle. The analytical models of the baffle at free surface are established, respectively. Firstly, the liquid domain is divided into several liquid subdomains has continuous boundary conditions of class C1 by introducing artificial interfaces. Based on the superposition principle, the formal solution of the velocity potential of each liquid subdomain is obtained using the separation of variables method. The formal solution is substituting into the interface between the subdomains and the free liquid surface condition gives the series equation with the determined coefficients. The spatial coordinates in the equation are eliminated by weighted integration, and the characteristic equation is obtained by truncating the equation. The sloshing frequency and mode obtained by the characteristic equation. The total velocity potential function under lateral excitation is taken as the sum of the container potential function and the liquid perturbed potential function. The dynamic response equation with generalized coordinates can be obtained by substituting the perturbation velocity potential and rigid body velocity potential into the wave equation of liquid surface. The sloshing response of liquid in the container is obtained by solving the equation.
关键词
竖向隔板 /
矩形储箱 /
水平激励 /
刚体速度势 /
摄动速度势
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Key words
vertical baffle /
rectangular container /
horizontal excitation /
the container potential function /
the liquid perturbed potential function
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