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剪切流作用下层合梁非线性振动特性研究

刘昊 瞿叶高 孟光

刘昊, 瞿叶高, 孟光. 剪切流作用下层合梁非线性振动特性研究. 力学学报, 2022, 54(6): 1669-1679 doi: 10.6052/0459-1879-22-114
引用本文: 刘昊, 瞿叶高, 孟光. 剪切流作用下层合梁非线性振动特性研究. 力学学报, 2022, 54(6): 1669-1679 doi: 10.6052/0459-1879-22-114
Liu Hao, Qu Yegao, Meng Guang. A numerical study on flapping dynamics of a composite laminated beam in shear flow. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1669-1679 doi: 10.6052/0459-1879-22-114
Citation: Liu Hao, Qu Yegao, Meng Guang. A numerical study on flapping dynamics of a composite laminated beam in shear flow. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1669-1679 doi: 10.6052/0459-1879-22-114

剪切流作用下层合梁非线性振动特性研究

doi: 10.6052/0459-1879-22-114
基金项目: 国家自然科学基金(U2141244, 11922208, 11932011, 12121002)和深蓝计划重点项目(SL2021 ZD104)资助
详细信息
    作者简介:

    瞿叶高, 教授, 主要研究方向: 非线性动力学与控制等. E-mail: quyegao@sjtu.edu.cn

  • 中图分类号: O352

A NUMERICAL STUDY ON FLAPPING DYNAMICS OF A COMPOSITE LAMINATED BEAM IN SHEAR FLOW

  • 摘要: 针对剪切流中层合梁的大变形非线性振动问题, 采用高阶剪切变形锯齿理论和冯·卡门应变描述层合梁的变形模式和几何非线性效应, 构建了大变形层合梁非线性振动有限元数值模型; 采用基于任意拉格朗日−欧拉方法的有限体积法求解不可压缩黏性流体纳维-斯托克斯方程, 结合层合梁和流体的耦合界面条件建立了剪切流作用下层合梁流固耦合非线性动力学数值模型, 采用分区并行强耦合方法对层合梁的流致非线性振动响应进行了迭代计算. 研究了不同速度分布的剪切流作用下单层梁和多层复合材料梁的振动响应特性, 并验证了本文数值建模方法的有效性. 结果表明: 剪切流作用下单层梁的振动特性与均匀流作用下的情况不同, 梁的运动轨迹受剪切流影响向下偏斜, 随着速度分布系数增加, 尾部流场中的涡结构发生改变; 刚度比对剪切流作用下层合梁的振动特性有显著影响, 随着刚度比的增加, 层合梁振动的振幅增大, 主导频率下降, 运动轨迹由‘8’字形逐渐变得不对称; 发现了不同厚度比和铺层角度情况下, 层合梁存在定点稳定模式、周期极限环振动模式和非周期振动模式三种不同的振动模式, 改变层合梁铺层角度可实现层合梁周期极限环振动模式向非周期振动模式转变.

     

  • 图  1  计算模型

    Figure  1.  Computational model

    图  2  复合材料层合梁的示意图

    Figure  2.  Schematic diagram of composite laminated beam

    图  3  双向流固耦合计算流程图

    Figure  3.  Flowchart of bidirectional fluid-structure interaction

    图  4  流场非结构网格C

    Figure  4.  Overview of the Mesh C

    图  5  不同$ \varDelta $情况下, 层合梁右端(x = L)节点横向位移的最大振幅

    Figure  5.  Maximum amplitude of transverse displacement at laminated beam tip as a function of $ \varDelta $

    图  6  不同$ \varDelta $情况下, 层合梁右端(x = L)节点横向位移的主导频率

    Figure  6.  Dominant frequency of transverse displacement at laminated beam tip as a function of $\varDelta $

    图  7  不同$ \alpha $情况下的来流速度分布

    Figure  7.  Velocity profile as a function of $\alpha $

    图  8  单层梁右端(x = L)节点的横向位移标准差曲线和平均值曲线

    Figure  8.  Standard deviation and mean value of transverse displacement at single isotropic beam tip as a function of $\alpha $

    图  9  单层梁右端(x = L)节点的横向振动频率曲线

    Figure  9.  Dominant frequency of transverse displacement at single isotropic beam tip as a function of $\alpha $

    图  10  单层梁在一个完整振动周期内的变形包络图

    Figure  10.  Deformation envelope of single isotropic beam in a complete motion period

    图  11  单层梁不同位置节点在5个振动周期内的横向位移时域曲线($\alpha $= 1)

    Figure  11.  Time domain responses of transverse displacement of beam at different positions in 5 flapping motion periods ($\alpha $= 1)

    图  12  不同$\alpha $情况下, 单层梁在20个完整振动周期内的右端节点位移Lissajous曲线

    Figure  12.  Lissajous curves of single isotropic beam in 20 flapping motion periods at beam tip with different $\alpha $

    图  13  一个完整振动周期内的涡量图($\alpha $= 0)

    Figure  13.  Vorticity diagrams in a complete flapping motion period at $\alpha $= 0

    图  14  一个完整振动周期内的涡量图($\alpha $= 0.5)

    Figure  14.  Vorticity diagrams in a complete flapping motion period at $\alpha $= 0.5

    图  15  一个完整振动周期内的涡量图($\alpha $= 1.8)

    Figure  15.  Vorticity diagrams in a complete flapping motion period at $\alpha $= 1.8

    图  16  层合梁右端(x = L)节点的横向位移时域响应

    Figure  16.  Time domain response of transverse displacement at beam tip

    图  17  层合梁右端(x = L)节点位移的Lissajous曲线

    Figure  17.  Lissajous curves of displacements at beam tip

    图  18  层合梁右端(x = L)节点的横向位移标准差曲线以及$ \gamma $= 0.33, $ \gamma $= 1时的变形包络图

    Figure  18.  Standard deviation of transverse displacement at beam tip as a function of $ \gamma $ and deformation envelope of beam at $ \gamma $= 0.33, $ \gamma $= 1, respectively

    图  19  层合梁右端(x = L)节点的横向位移平均值曲线

    Figure  19.  Mean value of transverse displacement at beam tip as a function of $ \gamma $

    图  20  层合梁右端(x = L)节点的横向位移标准差曲线以及$ \theta $= 35°, $ \theta $= 40°时的时域曲线

    Figure  20.  Standard deviation of transverse displacement at beam tip as a function of $ \theta $ and time domain response at $ \theta $= 35°, $ \theta $= 40°, respectively

    图  21  层合梁右端(x = L)节点的横向位移平均值曲线以及$ \theta $= 35°, $ \theta $= 40°时的Lissajous曲线

    Figure  21.  Mean value of transverse displacement at beam tip as a function of $ \theta $ and Lissajous curves at $ \theta $= 35°, $ \theta $= 40°, respectively

    表  1  网格收敛性分析

    Table  1.   Grid independence test

    Amplitude ($ u_y / L $)Frequency ($ {{fL} \mathord{\left/ {\vphantom {{fL} {{U_0}}}} \right. } {{U_0}}} $)
    Mesh A0.077210.8917
    Mesh B0.078100.8914
    Mesh C0.080180.8903
    Ref. [13]0.082210.8789
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-03-21
  • 录用日期:  2022-05-23
  • 网络出版日期:  2022-05-24
  • 刊出日期:  2022-06-18

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