论文标题
相位滞后预测液体渗透实验中的非线性响应最大值
Phase-lag predicts nonlinear response maxima in liquid-sloshing experiments
论文作者
论文摘要
质量弹簧模型对于描述工程中的晃动共振至关重要。通过实验测量水平振荡的矩形储罐中液体的质量中心，我们表明低振幅宽度呈粘合剂遵守行驶方程。观察到响应曲线与软弹簧的弯曲，随着驱动振幅的增加，磁滞的增长。在很大的幅度下，出现复杂的波模式（包括在坦克壁上的波浪和跑步），观察到流量状态之间的竞争，动力学逐渐偏离了行李。我们还提供了基于潜在流程理论（Faltinsen＆Timokha 2009）的多模型模型的预测波形和响应曲线的定量比较，并表明它系统地高估了悬念幅度和磁滞。我们发现，液体质量中心与强迫之间的相位滞后是非线性响应最大值的关键预测指标。相位滞后完全反映了与悬挂动力学的偏差的发作，并且 - 最重要的是 - 在共振时，悬浮运动始终落后于90°（独立于波模式）。这确认了理论上的90°相线标准（Cenedese＆Haller 2020）。
Mass-spring models are essential for the description of sloshing resonances in engineering. By experimentally measuring the liquid's centre of mass in a horizontally oscillated rectangular tank, we show that low-amplitude sloshing obeys the Duffing equation. A bending of the response curve in analogy to a softening spring is observed, with growing hysteresis as the driving amplitude increases. At large amplitudes, complex wave patterns emerge (including wave-breaking and run up at the tank walls), competition between flow states is observed and the dynamics departs progressively from Duffing. We also provide a quantitative comparison of wave shapes and response curves to the predictions of a multimodal model based on potential flow theory (Faltinsen & Timokha 2009) and show that it systematically overestimates the sloshing amplitudes and the hysteresis. We find that the phase-lag between the liquid's centre of mass and the forcing is the key predictor of the nonlinear response maxima. The phase-lag reflects precisely the onset of deviations from Duffing dynamics and - most importantly - at resonance the sloshing motion always lags the driving by 90° (independently of the wave pattern). This confirms the theoretical 90°-phase-lag criterion (Cenedese & Haller 2020).
