论文部分内容阅读
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.
Combining with the concept of curvature in material mechanics, using the Grossman theory to calculate the aerodynamic force, a nonlinear dynamic model of a large aspect ratio airfoil is established by using Lagrange’s equation.The dimensionless model is adopted to deal with this model, The first Lyapunov quantity was used to study the critical conditions and paths for the evolution of the system from the steady-state equilibrium solution to the Hopf bifurcation (chattering motion) as well as the occurrence of benign chattering (supercritical), catastrophic chattering (subcritical ), The chattering behavior of the model was studied by using the normative theory and the Hopf bifurcation theorem, and the influence of different aspect ratios on the chatter vibration velocity was studied. The numerical simulation validated the theoretical analysis.