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在竖直振动的圆柱形容器中,利用理想流体中两时间尺度奇摄动展开法,研究了包括表面张力影响的自由面单一表面驻波的运动.通过求解势流方程,获得了一个包含三阶非线性项、外激励及表面张力影响的非线性振幅方程.结果表明当驱动频率较低时,表面张力对表面波模式选择不重要;然而,当驱动频率较高时,表面张力的影响是不可忽略的.说明表面张力具有使得自由面返回到平衡位置的作用.另外,由于考虑了表面张力的影响,使得理论结果比无表面张力时更加接近先前的实验结果.
In a vertically vibrating cylindrical vessel, the motion of a free surface single surface standing wave, including the influence of surface tension, is studied by using two time-scale odd perturbation expansion methods in an ideal fluid. By solving the potential flow equation, Nonlinearity equations of order nonlinearity, external excitation and surface tension show that the surface tension is unimportant for surface wave mode selection when driving frequency is low. However, when the driving frequency is high, the effect of surface tension is Can not be neglected, indicating that the surface tension has the effect of returning the free surface to the equilibrium position, and that the theoretical result is closer to the previous experimental result than the non-surface tension due to the influence of the surface tension.