目的 针对参数晃动失稳问题,研究充液容器竖直激励下的液面参数失稳特性,为充液容器抗晃动安全设计提供依据。方法 以刚性二维方形充液容器为对象,基于势流小幅晃动假设推导带阻尼马蒂厄控制方程,采用多尺度摄动法、能量增长系数法开展稳定性分析。摄动法解析次谐波与谐波失稳边界,揭示阻尼对不稳定区域的抑制规律。能量增长系数从扰动能量角度量化失稳演化强度,弥补摄动法仅能判别失稳与否的局限。同时搭建包含激振、激光液面测振、加速度采集功能的试验平台,以10 cm充液高度方腔为试验对象,实测前四阶晃动模态固有频率与阻尼比,通过扫频变幅值试验获取失稳边界、模态共存区间,并测试0.2g、0.3g、0.4g激励下各阶模态稳态波高。结果 同阶模态失稳平衡波高随激励加速度增大而升高,同等激励下,低阶次谐波晃动幅值远高于高阶模态,一阶模态在0.4g激励下波高达充液高度82.2%,危害性最为突出。结论 本文融合多尺度摄动法与能量增长系数法,实现了失稳边界判定与晃动强度评估的有效互补,研究成果可为充液容器抗参数晃动安全设计提供可靠的理论与试验支撑。
Abstract
To solve the problem of parameter sloshing instability, the work aims to investigate the free-surface parameter instability characteristics of liquid-filled containers under vertical excitation, so as to provide a basis for the anti-sloshing safety design of liquid-filled containers. With a rigid two-dimensional square liquid-filled container as the research object, the damped Mathieu governing equation was derived based on the potential flow assumption for small-amplitude sloshing, and the stability analysis was conducted via the multi-scale perturbation method and energy growth coefficient method. Specifically, the perturbation method was adopted to resolve the instability boundaries of subharmonic and harmonic responses and reveal the suppression law of damping on unstable regions. The energy growth coefficient quantified the evolution intensity of instability from the perspective of perturbation energy, making up for the limitation that the perturbation method could only judge whether instability occurred. An experimental platform integrated with vibration excitation, laser liquid surface vibration measurement and acceleration acquisition systems was established. Experiments were carried out on a square cavity with a liquid filling height of 10 cm. The natural frequencies and damping ratios of the first four sloshing modes were measured. Sweep-frequency and variable-amplitude tests were performed to obtain instability boundaries and mode coexistence intervals, and the steady-state wave heights of each mode under excitation of 0.2g, 0.3g and 0.4g were tested. The equilibrium wave height of a single mode after instability rose with the increase of excitation acceleration. Under identical excitation levels, the sloshing amplitude of low-order subharmonics is much larger than that of high-order modes. The wave height of the first-order mode reaches 82.2% of the liquid filling height under 0.4g excitation, which poses the most prominent hazard. This paper combines two theoretical methods to realize complementary evaluation of instability boundary identification and sloshing intensity quantification, and can provide theoretical and experimental support for the safety design of liquid-filled containers against parametric sloshing.
关键词
充液容器 /
摄动法 /
能量增长 /
参数晃动试验 /
垂直激励 /
参数失稳
Key words
liquid-filled containers /
perturbation method /
energy growth /
parameter sloshing test /
vertical excitation /
parameter instability
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