Autoparametric resonances in elastic structures carrying two rectangular tanks partially filled with liquid
Autoparametric resonances in elastic structures carrying two rectangular tanks partially filled with liquid
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DOI：
10.1016/j.jsv.2006.11.037
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发表时间：
2007-05
影响因子：
4.7
通讯作者：
T. Ikeda
中科院分区：
文献类型：
--
作者：
T. Ikeda
研究了载液罐弹性结构在垂直谐波激励下的非线性振动问题。在两个矩形液罐中，结构的固有频率与晃动的最低固有频率之间满足2:1:1的内共振比。这里的理论分析仅限于二维流动，没有考虑三维法拉第波。同时假定流体深度是有限的。考虑了水动力的非线性，采用伽辽金方法推导了运动模态方程。然后用范德波尔法确定频率响应曲线。讨论了液面和内共振比偏差（即失谐）对频率响应曲线的影响。因此，我们得到的结果与在单充液罐结构下得到的结果不同。根据液面和激励频率的不同，可以产生两种类型的振动：单模溶液（在任何一个槽内晃动）和双模溶液（在两个槽内晃动）。当内部共振比存在一定偏差时，对应于单模解的频响曲线分支上出现含混沌振动的调幅和调相运动。通过实验验证了理论结果的有效性。
Nonlinear vibrations of elastic structures carrying two liquid-filled tanks under vertical harmonic excitation are investigated. A 2:1:1 ratio of internal resonance is satisfied between the natural frequency of the structure and the lowest natural frequencies of sloshing in two rectangular liquid tanks. The theoretical analysis here is restricted to two-dimensional flow and three-dimensional Faraday waves are not considered. The finite fluid depths are also assumed. Modal equations of motion are derived by using Galerkin's method, taking into account the nonlinearity of the hydrodynamic force. Then, frequency response curves are determined by using van der Pol's method. The respective influences of the liquid levels and the deviation of the internal resonance ratio (i.e., the mistuning) on the frequency response curves are demonstrated. As a result, we have obtained results different from those obtained in the case of a structure with a single liquid-filled tank. It is found that two types of vibrations can occur depending on the liquid levels and the excitation frequency: a single-mode solution (sloshing in either tank) and a double-mode solution (sloshing in both tanks). Amplitude- and phase-modulated motion including chaotic vibrations appears on the branches of the frequency response curves, which correspond to the single mode solution, when some deviation of the internal resonance ratio exists. The validity of the theoretical results was verified by the experiments.