基于非均匀梁模型的二维柔性机翼固有振动分析
Natural vibration analysis of two-dimensional flexible wing based onnon-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，因此结构的分布形式将直接影响其固有动力学特性，最终改变其气动弹性性能。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的等效建模方法，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的等效建模方法，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 silica gel skin material. The Young's modulus of the 3D printing material and silica gel skin material 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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