基于碰撞振动系统的液体晃动非线性动力学分析

Nonlinear Dynamic Analysisof Liquid Sloshing Based onan Impact Vibration System

摘要: 液体晃动广泛存在于大型充液航天器、带储罐的重型车辆和船舶等运载工具中，随着航天事业的快速发展，现代航天器通常需要携带大量的液体燃料，而液体晃动会影响航天器的姿态稳定性和控制精度，因此研究充液储罐在不同激励下的动力学行为对实现航天器的稳定控制至关重要。在航天器的姿态变化过程中，由于惯性力和重力的作用，会导致液体燃料发生剧烈晃动，并伴随着对罐壁的碰撞作用。因此本文依据经典的双侧约束碰撞振动系统建立液体晃动等效力学模型，利用庞加莱映射理论对系统的外激励幅值和频率进行研究，研究表明在不同的参数影响下，系统出现丰富的动力学行为。随着参数的变化，系统呈现出周期运动和混沌运动的交替出现，在一定参数条件下，系统还表现出擦边分岔、倍周期分岔等非线性现象。该研究为后续航天器液体晃动的非线性动力学分析提供了基础。

Abstract: Liquid sloshing is widely present in vehicles such as large liquid-filled spacecraft, heavy vehicles with tanks, and ships. With the rapid advancement of the aerospace industry, modern spacecraft often needs to carry a large amount of liquid fuel, and liquid sloshing can affect the attitude stability and control precision of the spacecraft. Therefore, studying the dynamic behavior of liquid-filled tanks under different excitations is crucial for achieving stable control of spacecraft. During the attitude adjustment process of a spacecraft, the inertial and gravitational forces can cause the liquid fuel to slosh violently, accompanied by impacts against the tank walls. Consequently, this paper establishes an equivalent mechanical model for liquid sloshing based on the classical vibro-impact system with bilateral constraints. Using Poincaré map theory, the amplitude and frequency of the external excitation are investigated. The research indicates that under the influence of different parameters, the system exhibits rich dynamic behaviors. As parameters vary, the system demonstrates an alternation between periodic and chaotic motions. Under certain parameter conditions, the system also presents nonlinear phenomena such as grazing bifurcation and period-doubling bifurcation. This study provides a foundation for subsequent nonlinear dynamic analysis of liquid sloshing in spacecraft.