| 带控制面机翼结构基于弧长数值连续法的颤振特征研究 |
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| 引用本文： | 陈恒,王扬渝,金江明.带控制面机翼结构基于弧长数值连续法的颤振特征研究[J].应用数学和力学,2017,38(7):769-779. |
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| 作者姓名： | 陈恒 王扬渝 金江明 |
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| 作者单位： | 浙江工业大学 机械工程学院, 杭州 310014 |
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| 基金项目： | The National Natural Science Foundation of China(51405440)国家自然科学基金(51405440)，浙江省自然科学基金(LY13E050018) |
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| 摘 要： | 以三自由度二元机翼为研究对象，将浮沉位移和俯仰位移方向的非线性刚度简化为立方非线性，对于存在间隙的控制面采用双线性刚度代替.考虑准定常气流，建立气动弹性运动方程，通过数值模拟构造峰值-峰值图，反映其在不同气流速度下的振动特征.通过弧长数值连续法构造系统的分岔图，结合Floquet算子研究其稳定性及其分岔类型，所得分岔图和数值模拟的结果相吻合.由分岔图可得系统由于控制面双线性的存在，导致机翼结构振动形态多变，存在多个分岔点和多个不稳定区间，不仅存在极限环振动和非光滑准周期振动，而且在某些不稳定区间出现混沌现象.
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| 关 键 词： | 气动弹性系统 峰值-峰值图 数值连续法 极限环 分岔 |
| 收稿时间： | 2016-07-21 |
Flutter Characteristics Analysis of 2D Rigid Airfoils With Control Surface Based on the Arc-Length Numerical Continuation Method |
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| CHEN Heng,WANG Yang-yu,JIN Jiang-ming.Flutter Characteristics Analysis of 2D Rigid Airfoils With Control Surface Based on the Arc-Length Numerical Continuation Method[J].Applied Mathematics and Mechanics,2017,38(7):769-779. |
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| Authors: | CHEN Heng WANG Yang-yu JIN Jiang-ming |
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| Affiliation: | College of Mechanical Engineering, Zhejiang University of Technology,Hangzhou 310014, P.R.China |
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| Abstract: | A 3-DOF aeroelastic model was built for 2D rigid airfoils with control surface.This model was simplified with cubic nonlinear stiffness in heave and pitch,where the freeplay control surface was replaced with bilinear stiffness.According to the quasi-steady aerodynamic theory,the motion equations for the system was established.The peak-to-peak value diagram was used to depict the global dynamic properties of the airfoil at different flow velocities,and the arc-length numerical continuation method together with the Floquet multiplier was applied to construct the bifurcation diagram and study the aerodynamic stability.The bifurcation diagram matched the peak-to-peak value diagram well.The results show there are various dynamic behaviors due to freeplay nonlinearity.The aeroelastic model yields complicated limit cycle oscillations,quasi-periodic motions and chaotic phenomena when the angular displacement of the control surface reaches the clearance limit. |
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| Keywords: | aeroelasticity peak-to-peak value diagram numerical continuation method limit cycle bifurcation |
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