A NUMERICAL STUDY ON FLAPPING DYNAMICS OF A COMPOSITE LAMINATED BEAM IN SHEAR FLOW
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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.Abstract: We present a numerical study of the large deflection flapping dynamics of a composite laminated beam in a shear axial flow. A higher-order shear deformation zig-zag theory combined with von Kármán strains is adopted to characterize the geometrical nonlinearity of the composite laminated beam. The finite volume method based on an arbitrary Lagrangian-Eulerian (ALE) approach is employed to solve the Navier-Stokes equation of incompressible viscous fluid. A strongly coupled, partitioned fluid-structure interaction method is adopted to accommodate the dynamic coupling of the two-dimensional shear flow and the laminated beam. The validity of the present method is confirmed by analysing the flapping characteristics of composite laminated beams, which with difference in elasticity between the two layers, subjected to a uniform axial flow. We investigate the effects of shear velocity profile on the flapping characteristics (including limit-cycle oscillation, vortex shedding frequency, and flow pattern) of single isotropic beams and composite laminated beams in a shear axial flow. It is found that with the increase of shear velocity slope, the deflection of the flapping motion neutral axis increases, the standard deviation and dominant frequency of transverse flapping displacement at the beam tip first decrease and then increase. In addition, the differences in the wake vortex modes are discussed. The flapping characteristics of laminated beams with difference in elastic modulus, thickness and ply angle between the two layers are studied. The increase of the difference in elastic modulus changes the symmetry of the laminated beam flapping motion trajectory. Three distinct response regimes are observed depending on the difference in thickness and ply angle between the two layers: fixed-point stable regime, periodic limit-cycle oscillations regime, and aperiodic oscillations regime. The change of thickness ratio of laminated beams makes its vibration regime change from periodic limit cycle oscillations regime to fixed-point stable regime. The increase of the ply angle of laminated beams changes the flapping regime from periodic limit cycle oscillations regime to aperiodic oscillations regime.
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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 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 -
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