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Study on Nonlinear Vibrations of Structures Carrying Liquid Tanks

液罐运载结构非线性振动研究

基本信息

批准号：
10650244
负责人：
IKEDA Takashi
金额：
$ 1.79万
依托单位：
Shimane University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10650244/
关键词：
Vibration Coupled with Liquid Motion Sloshing Cylindrical Tank Nonlinear Vibration Sinusoidal Excitation Resonance Curve Amplitude-Modulated Motion Liquid Damper 鉛直正弦加振

项目摘要

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.

本文研究了圆柱形贮箱中弹性结构的垂直激励与液体晃动的非线性耦合振动。当结构的固有频率接近晃动固有频率的两倍时，该系统表现出自参数系统的行为。我们治疗了两个病例，即，当晃动模态的轴对称模态或反对称模态占主导时，并给出了谐振曲线。主要研究结果如下：1.在理论分析中，考虑液动力的非线性，从系统的运动方程出发，推导出系统的模态方程。然后利用谐波平衡法和FFT分析得到了共振曲线的表达式。2.在调谐条件下，结构和液体表面分别发生简谐振动和1/2阶亚谐振动，使得结构的固有频率和液体晃动的固有频率满足关系2：1.3.随着液位的降低，结构的共振曲线形状由尖峰形变为平坦形。4.调谐条件的一定偏差可能引起调幅运动。通过引入失谐参数，例如，σ D201 D2=p D20 D2-2p D201 D2（p D 20 D 2为结构的固有频率，p D 201 D 2为轴对称晃动模态的固有频率），这种运动只有在高液位且σ D 201 D 2 <0.5时才能出现。理论谐振曲线与实验结果定性地吻合得很好。此外，还观察到调幅运动。