Aeroelastic Instability of Variable-Stiffness Panels with Curvilinear Fibers in Subsonic Flow
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摘要:
针对曲线纤维变刚度复合材料层合板在高速列车壁板结构轻量化设计中的广阔应用前景，研究了弹性、黏弹性变刚度复合壁板在亚音速流场中的气动弹性稳定性问题. 首先，基于Mindlin厚板理论和势流流动理论分别描述壁板结构变形和亚音速气动力，根据虚功原理和有限元法建立了曲线纤维变刚度复合材料弹性/黏弹性壁板的气动弹性稳定性分析模型，进而采用复模态理论求解复合材料变刚度壁板发散临界速度；在验证方法正确性和收敛性的基础上，研究了壁板关键参数等对复合变刚度壁板发散失稳特性的影响规律. 研究结果表明：与直线纤维壁板相比，通过调整曲线纤维路径可以实现壁板的发散临界速度50%左右的提升，有效增强壁板气动弹性稳定性.
Abstract:In view of the extensive application of curved fiber composite laminates in the lightweight design of high-speed train structures, the aeroelastic stability of elastic and viscoelastic variable-stiffness composite panels in a subsonic flow field was studied. First, classical thick theory along with a Mindlin plate was adopted for structural modeling and potential flow theory for aerodynamic modeling. An aeroelastic model of composite variable-stiffness panels with curvilinear fibers was then established adopting the principle of virtual work and the finite element method, which was solved using complex mode theory in the frequency domain. The divergence characteristics for key parameters were investigated following verification of the validity and convergence of the presented method. Numerical results show that, relative to the straight-fiber panel, the critical divergence speed can be increased by approximately 50% by varying the path orientations of the curvilinear fibers.
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Key words:
- aeroelastic stability /
- curvilinear fibers /
- variable stiffness /
- composite panels /
- subsonic flow
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图 2 曲线纤维壁板固有频率结果对比
注：每种图例下第一个柱状条为本文解，第二个柱状条为文献[12]解.
Figure 2. Comparison of natural frequencies of curved fiber composite laminates
图 3 黏弹性和弹性变刚度壁板频率随气流速度变化
Figure 3. Change of the two frequencies of viscoelastic and elastic variable-stiffness panels with air velocity
图 4 直线铺设与曲线铺设对变刚度壁板发散临界速度的影响
Figure 4. Comparison of variable-stiffness panel instability with straight and curved fiber laying
图 5 铺层主方向对曲线纤维变刚度壁板发散临界速度影响
Figure 5. Influence of ply direction on divergence critical speed of variable-stiffness panels with curved fibers
图 6 曲线纤维变刚度壁板失稳速度随T0的变化（T1不变）
Figure 6. Changes of divergence characteristics with T0 for variable-stiffness plate with curved fibers (T1 unchanged)
图 7 曲线纤维变刚度壁板失稳速度随T1的变化（T0不变）
Figure 7. Changes of flutter characteristics with T1 for variable-stiffness plate with curved fibers (T0 unchanged)
图 8 黏弹性阻尼对曲线纤维变刚度壁板发散临界速度影响
Figure 8. Influence of viscoelastic damp on divergence critical speed of variable-stiffness panels with curved fibers
图 9 约束对曲线纤维变刚度壁板发散失稳临界速度影响
Figure 9. Influence of boundary conditions on divergence critical speed of variable-stiffness panels with curved fibers
表 1 变刚度复合壁板固有频率的网格收敛性
Table 1. Grid convergence of natural frequencies of composite panels with variable stiffness
固有
频率网格规模 文献[12] 误差/% 5 × 5 10 × 10 20 × 20 30 × 30 一阶 3.786 4.060 3.936 3.937 3.941 0.10 二阶 5.853 5.278 5.126 5.090 5.087 0.06 三阶 13.087 7.848 7.582 7.532 7.565 0.43 四阶 16.219 11.012 10.740 10.358 10.385 0.26 五阶 17.409 12.281 10.978 10.658 11.052 3.56 六阶 22.249 12.274 11.939 11.697 11.327 3.27 
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表 2 两端固支壁板发散稳定性结果对比
Table 2. Divergence stability of the plate with bilateral fixation
厚度/
mm板长 0.8 m 板长 0.9 m 板长 1.0 m 文献 本文 文献 本文 文献 本文 2.40 73.53 71.03 61.62 61.01 52.61 53.01 2.60 82.90 80.25 69.48 68.51 59.23 59.10 2.90 97.66 95.47 81.84 81.06 69.88 70.04 3.30 118.55 116.67 99.35 98.21 84.82 85.12
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