纵向参数激励下平动刚-液耦合系统稳定性

纵向参数激励下液体晃动稳定性是航天器动力学中一个广受关注的问题,然而在以往的研究中没有考虑液体晃动与航天器运动之间的耦合作用对系统参数振动稳定性的影响.建立了用液体晃动等效单摆模型描述的纵向激励下平动刚-液耦合系统的Mathieu方程,采用摄动法确定了耦合系统1/2亚谐波振动和谐波振动的激励幅-频稳定性边界.研究发现,液体晃动与主刚体横向运动的耦合作用扩大了参数振动不稳定区,并使其向高频移动,影响的程度随等效晃动质量的减小而减小;液体晃动模态阻尼对1/2亚谐波振动不稳定区的缩小作用远弱于对谐波振动不稳定区的缩小作用.对耦合系统第1阶液体晃动模态1/2亚谐波振动响应的研究表明:当纵向激励参数在不稳定区内时,可能引起主刚体的纵横耦合振动现象.

PARAMETRIC STABILITY OF A TRANSLATIONAL RIGID-LIQUID COUPLED SYSTEM SUBJECT TO VERTICAL EXCITATIONS

Parametric stability of liquid sloshing under vertical excitations is widely concerned in spacecraft dynamics. However, the influence of the coupling between the liquid sloshing and the spacecraft motion on the parametric stability has not been investigated in the previous studies. In this paper, the Mathieu's equation of a translational rigid-liquid coupled system subject to vertical excitations is presented with the equivalent pendulum model of liquid sloshing. The one-half subharmonic and harmonic stability boundaries of the coupled system are analyzed using the perturbation method. It is illustrated that, the lateral coupling between the liquid sloshing and the rigid body motion enlarges the parametric unstable regions and enhances the resonance frequencies. The effects decline with the decrease of equivalent sloshing mass. Due to the linear slosh damping, the reduction of the one-half subharmonic unstable region is much less than that of the harmonic unstable region. The one-half subharmonic responses associated with the first sloshing mode of the coupled system show that, when the parameters of vertical excitations drop in the unstable region, the rigid body may experience a vertical-lateral coupling vibration.