Autoparametric resonances of elastic structures coupled with two sloshing modes in a square liquid tank, Transaction of the ASME
Autoparametric resonances of elastic structures coupled with two sloshing modes in a square liquid tank, Transaction of the ASME
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方形液体罐中弹性结构与两种晃动模式耦合的自参数共振，ASME 汇刊
DOI：
10.1115/1.4006531
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Y
中科院分区：
文献类型：
--
作者：
Ikeda;T.;Takashima;M.;Harata;Y
研究了受到垂直正弦激励的方形罐中与液体晃动耦合的弹性结构的非线性振动。理论分析中，结构固有频率与两种晃动模态之比满足2:1:1。利用伽辽金法推导了结构的运动方程和七种晃动模式，同时考虑了晃动的非线性。然后将线性阻尼项纳入模态方程以考虑晃动的阻尼效应。频率响应曲线是使用 van der Pol 方法确定的。研究了液位、罐体横截面长宽比、调谐条件偏差和激励幅度的影响。当液位较高时，根据激励频率，存在三种晃动模式： (i) (1,0) 和 (0,1) 晃动模式均以相同的幅度出现； (ii) 这两种模式出现在不同的幅度； (iii) 出现 (1,0) 或 (0,1) 模式。调谐条件的小偏差可能会导致发生 Hopf 分岔，随后出现包括混沌振动在内的调幅运动。还计算分岔集以说明系统参数对系统响应的影响。研究发现，对于低液位，方形调谐液体阻尼器 (TLD) 比矩形 TLD 更有效。还进行了实验以证实理论结果的有效性，并且与实验数据吻合良好。
Nonlinear vibrations of an elastic structure coupled with liquid sloshing in a square tank subjected to vertical sinusoidal excitation are investigated. In the theoretical analysis, the ratios of the natural frequencies of the structure and two sloshing modes satisfy 2:1:1. The equations of motion for the structure and seven sloshing modes are derived using Galerkin’s method while considering the nonlinearity of sloshing. The linear damping terms are then incorporated into the modal equations to consider the damping effect of sloshing. The frequency response curves are determined using van der Pol’s method. The influences of the liquid level, the aspect ratio of the tank cross-section, the deviation of the tuning condition, and the excitation amplitude are investigated. When the liquid level is high, and depending on the excitation frequency, there are three patterns of sloshing: (i) both (1,0) and (0,1) sloshing modes appear at identical amplitudes; (ii) these two modes appear at different amplitudes; and (iii) either (1,0) or (0,1) mode appears. Small deviations of the tuning condition may cause Hopf bifurcations to occur followed by amplitude modulated motion including chaotic vibrations. Bifurcation sets are also calculated to illustrate the influence of the system parameters on the response of the system. It is found that for low liquid levels, square tuned liquid dampers (TLDs) work more effectively than rectangular TLDs. Experiments were also conducted in order to confirm the validity of the theoretical results and were in good agreement with the experimental data.