# 多悬臂梁–流体的模态耦合与拍振研究Research on Modal Coupling and Slap Phenomenon of Multi-Cantilever Beam-Fluid Structure

• 全文下载: PDF(2150KB)    PP.179-186   DOI: 10.12677/IJM.2019.83020
• 下载量: 89  浏览量: 274   国度天然迷信基金支撑

In this paper, the modal analysis of multi-cantilever beam and fluid system is carried out by ANSYS code. The variations of wet frequencies of coupling system with the fluid width are obtained. The results agree well with the theoretical solutions. The beat vibration of multi-cantilever and fluid system is studied. In multi-cantilever beam and fluid system, not only there is interaction between beam and fluid, but also the interaction between the beams. The interaction effect between beams decreases with the increase of fluid width between beams. The difference of modal frequency caused by the interaction between beams results in beat vibration of multi-cantilever and fluid system. Because the different contributions of mode shapes are given to the displacement functions of different beams, the frequency and amplitude of beat vibration are generally different for the different beams.

1. 引言

2. 多悬臂梁–流体的模态耦合

2.1. 双悬悬臂梁–流体的模态耦合

Table 1. The first two frequencies of cantilever beam with one side infinite water

Figure 1. Double cantilever beam-fluid system

Figure 2. Frequency variation curve of two modes of the first order

Figure 3. Frequency variation curve of two modes of the second order

ANSYS模仿取得的曲线与文献 [3] 中实际解法取得的成果分歧，成果注解：两个梁构成的一个体系，其体系某一阶天然频率有两个，当梁间距较小时，由于液体的耦合感化，体系的两个频率产生了很大年夜变更，解释两个梁经过过程液体耦合产生了相互感化；随着梁间距增大年夜，2a/h大年夜于3时，体系的两个频率趋于直线，与单个梁与无穷水体感化的天然频率雷同，解释梁间的耦合感化趋于零。

2.2. 三悬臂梁–流体构造模态影响

Figure 4. Triple cantilever beam-fluid system

Figure 5. The three vibration shapes of the first mode shape for the system of triple cantilever beam and fluid

Figure 6. Variations of the three wet frequencies with liquid width L

3. 耦合自在振动的拍景象

3.1. 双梁–液系一切拍振景象

$\left\{\begin{array}{l}{u}_{a}\left(z,t\right)=\underset{i=1}{\overset{\infty }{\sum }}{q}_{i}{Y}_{ai}\left(z\right)\cdot \mathrm{cos}\left({\omega }_{i}\cdot t+{\phi }_{i}\right)\\ {u}_{b}\left(z,t\right)=\underset{i=1}{\overset{\infty }{\sum }}{q}_{i}{Y}_{bi}\left(z\right)\cdot \mathrm{cos}\left({\omega }_{i}\cdot t+{\phi }_{i}\right)\end{array}$ (1)

$\left\{\begin{array}{l}{u}_{a}\left(z,t\right)={q}_{1}{Y}_{a1}\left(z\right)\cdot \mathrm{cos}\left({\omega }_{1}^{\left(1\right)}\cdot t+{\phi }_{1}\right)+{q}_{2}{Y}_{a2}\left(z\right)\cdot \mathrm{cos}\left({\omega }_{1}^{\left(2\right)}\cdot t+{\phi }_{2}\right)\\ {u}_{b}\left(z,t\right)={q}_{1}{Y}_{b1}\left(z\right)\cdot \mathrm{cos}\left({\omega }_{1}^{\left(1\right)}\cdot t+{\phi }_{1}\right)+{q}_{2}{Y}_{b2}\left(z\right)\cdot \mathrm{cos}\left({\omega }_{1}^{\left(2\right)}\cdot t+{\phi }_{2}\right)\end{array}$ (2)

${u}_{a}\left(z,0\right)=Y\left(z\right)$ ; ${\frac{\text{d}{u}_{a}}{\text{d}t}|}_{t=0}={{u}_{b}|}_{t=0}={\frac{\text{d}{u}_{b}}{\text{d}t}|}_{t=0}=0$ (3)

$\left\{\begin{array}{l}{u}_{a}=Y\left(z\right)\mathrm{cos}\left(\frac{{\omega }_{1}^{\left(2\right)}-{\omega }_{1}^{\left(1\right)}}{2}\cdot t\right)\mathrm{cos}\left(\frac{{\omega }_{1}^{\left(2\right)}+{\omega }_{1}^{\left(1\right)}}{2}\cdot t\right)\\ {u}_{b}=-Y\left(z\right)\mathrm{sin}\left(\frac{{\omega }_{1}^{\left(2\right)}-{\omega }_{1}^{\left(1\right)}}{2}\cdot t\right)\mathrm{sin}\left(\frac{{\omega }_{1}^{\left(2\right)}+{\omega }_{1}^{\left(1\right)}}{2}\cdot t\right)\end{array}$ (4)

3.2. 三梁–液系一切拍振景象

4. 结论

1) 由于流固耦合感化的存在，悬臂梁之间存在相互感化，这类相互感化影响了耦联构造的湿模态，且这类影响随着梁间液体宽度的增长而减弱。

Figure 7. Beat vibration of double beam-fluid system

Figure 8. Beat vibration of triple beam-fluid system

2) 多悬臂梁–流体耦接洽统拍振景象是由梁间相互感化产生的模态频率差招致，由于不合模态对不合梁位移函数供献不合，不合梁的拍景象频率及振幅普通不合。

NOTES

*通信作者。

 [1] 郑哲敏, 马宗魁. 悬臂梁在一侧受有液体感化时的自在振动[J]. 力学学报, 1959, 3(2): 111-119. [2] 周叮. 两侧受液时悬臂梁的自在振动分析[J]. 工程力学, 1981, 8(3): 107-115. [3] 李遇春, 朱暾, 白冰. 悬臂梁–流体–悬臂梁耦接洽统的湿模态相互感化[J]. 工程力学, 1998, 15(1): 58-65. [4] Meirovitch, L. (1975) Elements of Vibra-tion Analysis. Second Edition, McGraw-Hill Book Company, New York, 125-129. [5] 李京颍. 拍景象的数值模仿分析[J]. 阜阳师范学院学报(天然迷信版), 2005, 22(3): 17-19. [6] 李遇春. 液体闲逛动力学基本[M]. 北京: 迷信出版社, 2017: 121-126. [7] 王新敏. ANSYS工程构造数值分析[M]. 北京: 人平易近交通出版社, 2007: 273-278.