针对矩形容器在匀加速运动下的液体晃动问题，采用基于非线性振动的解析方法求出容器所受液体晃动力的解析近似解，并分析其非线性效应以及加速度大小和充液率的影响作用。根据流体速度势的解析解计算边壁处的流体压力，而对于部分边壁区域的流体压力则采用线性分布的近似估计。对流体压力沿边壁做积分即可获得边壁处液体晃动力的解析近似解。计算结果表明，非线性因素并不会对容器所受晃动力产生较大影响，晃动力非线性项与加速度立方成正比；充液率的变化会使得线性晃动固有频率的数值发生改变，进而对晃动力线性项造成影响，其影响程度与固有频率曲线的变化趋势较为一致。
Abstract
For forced sloshing in a rectangular tank moving in a constant acceleration, an analytic method was proposed to solve analytical approximate solutions of sloshing forces on the tank based on the nonlinear vibration theory. Nonlinearity of sloshing and the effects of acceleration and filling rate were also analyzed. The liquid pressure on the sidewall was mainly calculated by the analytical solutions of fluid velocity potential, while in partial regions of sidewalls, the liquid pressure was approximately predicted by linear distribution. The analytical approximate solutions of sloshing force on the sidewalls were obtained by the integrations of liquid pressure along the sidewall. The results show that nonlinear factors do not have a major impact on the sloshing force on the tank; nonlinear term of sloshing force is proportional to the cube of accelerated speed; the fluctuation of filling rate will change the natural frequency of linear sloshing, and then make an impact to the nonlinear term of sloshing force, the impact is in agreement with the tendency of natural frequency curve.
关键词
晃动力 /
非线性 /
解析近似解 /
匀加速运动
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Key words
sloshing force /
nonlinearity /
analytical approximate solutions /
uniform acceleration motion
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