旋转层状液的自由震动(英文)

Free Oscillations of a Rotating Ideal Stratified Liquisds

考虑两种互不混合的理想不可压缩液体部分或全部充满刚体中在惯性力场中转动时的自由震动 ,在系统不受扰动时 ,其运动就象一个刚体 ,将其考虑成部分或完全充盈的刚体在惯性力场中的转动。确定层状液震动频谱就可归结为求解边界的特征值问题 ,这可以用解析的方法或数值的方法来求解。导出了在柱状空腔中快速旋转的两种互不混合的层状液边值问题的解析解。给出的不同半径处分层在不同充盈深度震动频率计算结果表明 :液体质量一定时分层液自震频率高于均质液 ;分层对某一平均半径内表面固有频率有决定性影响 。

In linear statement, free oscillations of two unmixed ideal incompressible liquids, partially or completely filling rigid body rotating in a field of mass forces is considered. Non perturbed motion is rotation of all system as one rigid body. The problem of a determination of a spectrum of frequencies of vibrations of stratified liquid is reduced to the solution of a boundary eigenvalue problem , that can be solved analytically or numerically. The exact solutions of the boundary problem for a cylindrical cavity in case of fast rotation are obtained.