一类大展弦比机翼非线性模型的稳定性与分岔

结合材料力学中曲率的概念,利用格罗斯曼理论计算气动力,应用拉格朗日方程建立了一类大展弦比机翼的非线性动力学模型.对该模型进行了无量纲化处理,利用第一李雅普诺夫量研究了该系统由稳态平衡解向Hopf分岔解(颤振运动)演化的临界条件和路径,以及系统发生benign颤振(超临界)、catastrophic颤振(次临界)的识别条件.利用规范性理论、Hopf分岔定理研究了模型的颤振行为,并研究了不同展弦比对颤振速度的影响.数值模拟验证了理论分析的结果.

Stability and bifurcation for a nonlinear model of high-aspect-retio wings

Combining the curvature concept in mechanics of materials with the Grossman theory to calculate the aeroelastic force, the nonlinear dynamic model of high-aspect-ratio wings was established by using Lagrange equation. The model was rewritten as dimensionless equations. The critical conditions and route for the stable solution to Hopf bifurcation solution were investigated by using the first Lyapunov quantity. The identification conditions for benign flutter and catastrophic flutter were obtained. The flutter is benign when the first Lyapunov quantity is negative, while the flutter is catastrophic when the first Lyapunov quantity is positive. The flutter was also studied by the normal form theory and Hopf bifurcation theory. The influence of different aspect ratio on the flutter speed was investigated. The results show that the flutter speed first decreases, then increases, and at last decreases as the aspect ratio increases. The Numerical Simulations were also given, which verify the analytical results.