Study on Nonlinear Vibrations of Structures Carrying Liquid Tanks

“一个弹性结构的垂直刺激和液体下沉在一个圆柱形坦克中的非线性偶联振动是被调查的。当一个结构的自然频率接近一个下降的自然频率两次时，这个系统就展示了一个自动参数化系统的行为。我们处理了两个案子，是的。当使用轴向模式或使用非对称模式时，通常使用倾斜模式。还有一条共振曲线已经准备好了。结果可以按以下方式概括：1.在理论分析中，模型方程是从控制系统的运动的部分方程中得出的，并采用非线性的液体力帐户。然后，通过使用谐波平衡和FFT分析的方法获得共振曲线的表达式。2.谐波振荡和1/2-oder亚谐波振荡可以在结构和液体表面上适当地占用，在结构的自然频率和液体衰减下，在调谐条件下，结构的自然频率和液体衰减有关系2 ：1.3.结构变化的形状从一个峰值到一个平坦的形状，作为一个液体水平的退化。4.A Tuning Condition的某些偏移可能会导致ampritude-modulated motions。根据研究参数的介绍，例如，伊D201伊D2=p伊D20伊D2- 2 p伊D201伊D2（Py D20 Y D2是结构的自然频率，Py D201 Y D2是轴向下沉模式的自然频率），这种运动只出现在高流体水平和Cy D201 Y D2<0.5.在实验中，理论上的共振曲线在良好的协议中具有良好的质量。在增加的、放大器调制的运动是可见的。

The nonlinear-coupled vibrations of an elastic structure vertically excited and liquid sloshing in a cylindrical tank are investigated. When the natural frequency of the structure is close to twice the natural frequency of the sloshing, this system exhibits the behavior of an autoparametric system. We treated two cases, i.e., when the axisymmetric mode or the anti-symmetric mode of sloshing mode occurs predominantly., and the resonance curves are presented. The results can be summarized as follows :1.In the theoretical analysis, the modal equations are derived from the partial equations of motion governing the system, taking account of the nonlinearly of liquid force. Then the expressions of the resonance curve are obtained by using the method of harmonic balance and an FFT analysis.2.Harmonic oscillations and 1/2-oder subharmonic oscillations can occur respectively in the structure and the liquid surface, under the tuning condition such that the natural frequencies of the structure and the liquid sloshing have the relation 2 : 1.3.The shape of the resonance curve for the structure changes from a shape with a peak to a flat shape, as the liquid level decreases.4.A certain deviation of the tuning condition may cause amplitude-modulated motions. By introducing the detuning parameter, e.g., σィイD201ィエD2=pィイD20ィエD2-2pィイD201ィエD2 (pィイD20ィエD2 is the natural frequency of the structure, and pィイD201ィエD2 is the natural frequency of the axisymmetric sloshing mode), this kind of motion can appear only for a high liquid level and σィイD201ィエD2<0.5.In the experiments, the theoretical resonance curves were qualitatively in good agreement with the experimental results. In addition, amplitude-modulated motions were observed.