容器匀加速运动状态下液体大幅晃动的解析计算

Analytic calculation of large-amplitude liquid sloshing in tank moving in uniform acceleration motion

针对矩形容器在匀加速运动下的液体受迫晃动问题,采用基于非线性振动的解析方法求出流体速度势和自由液面波高函数的解析近似解,并分析晃动非线性因素以及外部参数的影响作用.将晃动方程组无量纲化后,运用小参数法将其转化为若干线性偏微分方程组,再使用分离变量法求解.根据解析解表达式,揭示出自由液面波高函数非线性项和底部流体速度势非线性项的主要成分.分析结果表明,晃动非线性效应与加速度平方成正比;充液率的变化使得线性晃动固有频率的数值发生改变,进而对解析近似解造成影响,其影响程度由固有频率曲线的斜率决定.

For forced sloshing in a rectangular tank moving in a constant acceleration,an analytic method was proposed to solve analytical approximate solutions of fluid velocity potential and free surface elevation functions based on the nonlinear vibration theory.Nonlinear factors of sloshing and effects on external parameters were analyzed.Sloshing equations were non-dimensionalized,then transformed into some linear partial differential equations by the small parameter method.A variables separation method was used to solve these equations.Main components of nonlinear terms on the free surface elevation and fluid velocity potential functions at the bottom of the tank were revealed by expressions of analytical solutions.The analysis result shows that nonlinearity of sloshing is proportional to the square of the accelerated speed.The fluctuation of the filling rate can change the natural frequency of linear sloshing,and then make an impact to the analytical approximate solutions.The impact is depended on the slope of the natural frequency curve.