圆柱贮箱液体“平面”晃动波的稳定性研究  

INVESTIGATION OF STABILITY OF LIQUID PLANAR SLOSHING WAVE IN A CIRCULAR CYLINDRICAL TANK

作　　者：余延生[1] 马兴瑞 王本利[1] 

机构地区：[1]哈尔滨工业大学卫星技术研究所,哈尔滨150001 [2]中国航天科技集团,北京100830

出　　处：《振动与冲击》2008年第1期9-11,24,共4页Journal of Vibration and Shock

基　　金：国防十五预研资助项目(41320020301)

摘　　要：应用Floquet-Lyapunov方法研究了作水平横向运动圆柱贮箱中液体"平面"晃动波的稳定性问题。首先利用Narimanov-Moiseev三阶渐近假设关系,推导出描述液体作非线性共振晃动的5维渐近模态系统。根据此模态系统,推导出液体"平面"晃动波的频率响应方程并应用Floquet-Lyapunov方法研究了其稳定性和稳定区间。数值仿真结果表明虽然其频率响应方程与Duffing方程的频率响应方程具有相同的结构,但两者的稳定性范围有明显的不同。此外,当经过某一临界充液比时,液体的"平面"晃动将由"软"弹簧特性转变为"硬"弹簧特性。理论分析结果与实验有很好的吻合。Stability of liquid planar sloshing wave in a circular cylindrical tank with translational motion is investigated by Floquet-Lyapunov method.Five dimensional asymptotic modal system describing liquid nonlinear resonant sloshing is derived based on Narimanov-Moiseev third order asymptotic hypothesis.The frequency response equation describing liquid planar sloshing wave is derived and its stable region is studied by Floquet-Lyapunov method.The numerical simulation result indicates that although the frequency response equation has the same structure as Duffing equation's,their stable regions are different markedly.Furthermore, as liquid exceeds the critical depth,the'soft' spring characteristic of its planar sloshing is changed to'hard' spring characteristic.The theoretical results agree well with the experimental ones.

关 键 词：圆柱贮箱 “平面”晃动波 模态系统 幅频特性曲线 临界充液比 

分 类 号：O353.1[理学—流体力学]