NATURAL VIBRATION ANALYSIS OF TWO-DIMENSIONAL FLEXIBLE WING BASED ON NON-UNIFORM BEAM MODEL
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摘要: 变体飞行器通过光滑连续的结构变形改变气动特性, 从而提高飞行器的飞行性能, 具有很大的应用前景. 由于这类新概念飞行器主要通过改变自身结构形状以获得最佳工作性能的需求, 因此具有变形大、质量轻等特点, 较容易发生结构振动响应. 本文研究了一种以柔性变后缘作为变体形式的二维柔性机翼等效建模方法, 基于非均匀梁模型假设, 建立了该柔性翼的动力学模型. 通过利用Frobenius方法得到解析解及固有频率, 并用有限元方法进行对比验证, 发现前4阶固有频率的误差均在1%以内, 每阶固有频率对应的振型一致. 通过3D打印工程塑料ABS和硅胶蒙皮材料制备了柔性机翼结构件, 并通过动态测量法和拉伸试验分别测定了打印材料和硅胶蒙皮材料的杨氏模量, 搭建振动响应实验平台对制备的柔性机翼试验件进行振动试验. 对比发现模型振动试验获得的基频与理论模型结果一致, 并与有限元方法误差在3%以内. 本文通过理论分析和实验验证, 建立了二维柔性机翼等效建模方法, 研究结果将为柔性变后缘结构动力学特性分析及其控制应用方面提供理论支持.Abstract: In order to improve the flight performance of the aircraft, morphing technologies are used to change aerodynamic characteristics through smooth and continuous structural deformation. Since this new concept requires changing the structural shape to obtain the best performance, its inherent dynamic characteristics will be affected and even change its aeroelastic performance. In this paper, an equivalent modelling method of the two-dimensional flexible wing with camber morphing is developed. The dynamic model of the flexible wing is established based on the hypothesis of a non-uniform beam model. The analytical solution and natural frequencies are obtained by the method of Frobenius and verified by comparison with the finite element method solution. The errors of the first four natural frequencies are within 1% and the corresponding modes are consistent. The flexible wing is prepared by 3D printing engineering plastic (ABS) and silicone rubber skin. The Young's modulus of the 3D printing material and silicone rubber are respectively measured by dynamic measurement method and tensile test. The vibration response test platform is built to carry out vibration test of the flexible wing. It is found that the fundamental frequency obtained by vibration test is consistent with the theoretical model results, and the error is less than 3% compared with the finite element method. The equivalent modelling method of a two-dimensional flexible wing is established through theoretical analysis and experimental verification. The research results will provide theoretical support for applying the flexible trailing edge structures.
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Key words:
- FishBAC /
- camber variation /
- nonuniform beam /
- natural vibration /
- power series solution
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图 9 级数解与刚度拟合的阶数对频率的影响
Figure 9. Effect of order of series solution and stiffness fitting polynomial on frequency
9 级数解与刚度拟合的阶数对频率的影响(续)
9. Effect of order of series solution and stiffness fitting polynomial on frequency (continued)
图 10 ABS塑料动态法测杨氏模量实验实物图
Figure 10. Dynamic measurement test of Young's modulus of ABS plastic
图 12 硅胶单向拉伸实验应变-应力曲线
Figure 12. Strain-stress curve of silicone rubber in uniaxial tensile test
图 13 动态法测FishBAC固有频率实验实物图
Figure 13. Dynamic measurement test of the natural frequency of FishBAC flexible section
图 14 动态法测量FishBAC固有频率的实验结果
Figure 14. Dynamic measurement test results of the natural frequency of FishBAC
表 1 鱼骨柔性翼段模型参数
Table 1. Model parameters of the FishBAC morphing concept
Parameters Value baseline airfoil NACA0012 chord c/mm 305 span b/mm 150 start of morph xS/mm 107 end of morph xE/mm 260 number of stringer pairs n 14 stringer thickness tst/mm 0.8 skin thickness tsk/mm 1.5 spine thickness tbs/mm 2 stringer modulus Est/GPa 2.14 spine modulus Ebs/GPa 2.14 spine Poisson's ratio νbs 0.4 spine density ρbs/(kg·m−3) 1010 skin modulus Esk/MPa 4.56 skin Poisson's ratio νsk 0.4 skin density ρsk/(kg·m−3) 1010 
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表 2 验证算例参数
Table 2. Parameters of verification example
Parameters Value length l/mm 152.5 density ρ/(kg·m−3) 2700 width b/mm 1 thickness t/mm 2 Poisson's ratio ν 0.4 modulus of elasticity E/GPa 2.14
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表 3 等截面悬臂梁的频率(Hz)
Table 3. Frequency of cantilever beam with equal section (Hz)
Methods Vibration order 1 2 3 4 Euler beam solution 12.3679 77.5085 217.025 425.283 Euler exact solution 12.3678 77.3732 217.022 425.280 shear beam series solution 12.3656 77.4313 216.513 423.434 FEM (NASTRAN) 12.3665 77.4470 216.619 423.817
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表 4 FishBAC柔性段的频率(Hz)
Table 4. Frequency of the FishBAC (Hz)
Methods Vibration order 1 2 3 4 FEM (shell) 22.7621 118.163 292.228 — FEM (beam) 24.4647 136.962 368.522 709.733 Euler beam series solution 24.5482 138.507 373.935 725.166 shear beam series solution 24.5339 138.151 371.708 717.439
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表 5 材料特性实验结果
Table 5. Experimental results of material properties
Parameters Value modulus of elasticity (ABS plastics) E1/GPa 1.823 modulus of elasticity (silicone rubber) E2/MPa 2.919
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表 6 FishBAC柔性段的固有频率(Hz)
Table 6. The natural frequency of FishBAC (Hz)
Methods Frequency dynamic measurement test 19.4521 FEM (shell element) 18.5898 Euler beam series solution 19.9821 shear beam series solution 19.9654
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