摘要
利用奇异摄动理论的两时间变量展开法 ,研究了垂直强迫激励圆柱形容器中的单一水表面驻波模式。假设流体是无粘、不可压且运动是无旋的 ,在忽略了表面张力的影响下 ,得到一个具有立方项以及底部驱动项影响的非线性振幅方程。对上述方程进行了数值计算 ,并研究了特定 (3,4 )模式的表面驻波结构和特性 ,如驻波的节点分布及随某些参数的变化规律等 ,从计算的等高线的图象来看 。
This paper studys the single standing wave mode in a circular cylinder which is subjected to a vertical oscillation, employing two-time scales singular perturbation expansion. It is assumed that the fluid in circular cylindrical vessel is inviscid incompressible and the motion is irrotational. A dimensionless nonlinear evolution equation of slowly varying complex amplitude is derived without considering the effect of surface tension. The nonlinear amplitude equation is similar to a cubic nonlinear Schr dinger equation and incorporates the effect of parametric excitation. The standing surface wave's structures and characteristics of (3, 4) mode, such as the distribution of nodes and variable rules as the function of some parameters, is studied with the help of numerical computation. The contour of the free surface displacement agrees better with the results of experiment under the same condition.
出处
《应用力学学报》
CAS
CSCD
北大核心
2004年第1期5-12,共8页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金资助项目 ( 19772 0 63
19772 0 68)
