学术
低重环境下液体非线性晃动的稳态响应
贺元军[1,3] 马兴瑞[2] 王本利[1]
[1]哈尔滨工业大学卫星技术研究所,哈尔滨150002 [2]中国航天科技集团,北京100830 [3]四川航天技术研究院研发中心,成都610100
摘 要:
在俯仰激励作用下，圆柱贮箱中液体晃动存在平面运动、旋转运动和平面运动中的旋转运动等，而这些运动的稳定、不稳定区间的分界线与贮箱的半径、充液深度、重力强度、表面张力系数和晃动阻尼等基本系统参数有关,据此，首先建立了液体非线性晃动的微分方程组，并借助变分原理建立了液体压力体积分形式的Lagrange函数；然后将速度势函数在自由液面处作波高函数的级数展开，通过变分从而导出自由液面运动学和动力学边界条件非线性方程组；最后用多尺度法求解非线性方程组，就重力强度对圆柱形贮箱中液体非线性晃动的全局稳态响应的影响进行了详细的理论分析，并发现系统软硬特性的变化、跳跃和滞后等非线性现象．[著者文摘]
文章出处:
《应用数学和力学》-2007年28卷10期 -1135-1145页
文献标识码:
A
文章编号:
1000-0887（2007）10-1135-11
Stable Response of the Low-Gravity Liquid Non-Linear Sloshing in a Circle Cylindrical Tank
HE Yuan-jun, MA Xing-rui, WANG Ben-li （ 1. Center of Satellite Technology, Harbin Institute of Technology, Harbin 150001, P. R. China; 2. China Aerospace Science and Technology Corporation, Beifing 100830, P. R. China; 3. R ＆ D, Sichuan Academy of Aerospace Technology, Chengdu 610100,P. R. China）
Abstract:
Under pitch excitation, the sloshing of liquid in circular cylindrical tank includes planar motion, rotary motion and rotary motion inside planar motion. The boundaries between stable motion and unstable motion depend on the radius of the tank, the liquid height, the gravitational intension, the surface tensor and the sloshing damping. The differential equations of nonlinear sloshing are built first. And by variational principle, the Lagrange function of liquid pressure is constructed in volume intergration form. Then the velocity potential function is expanded in series by wave height function at the free surface. The nonlinear equations with kinematics and dynamics free surface boundary condi- tions through variation are derived. At last, these equations are solved by multiple-scales method. The influence of Bond number on the global stable response of nonlinear liquid sloshing in circular cylinder tank is analyzed in detail. Variations of amplitude frequency response characterstics of the system with Bond, jump, lag and other nonlinear phenomena of liquid sloshing are investigated.[著者文摘]
Key words:
circle cylindrical tank; nonlinear sloshing; low-gravity; multiple scales; stable response
基金资助:
国防十五预研资助项目（41320020301）
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