考虑机翼几何非线性的气动弹性建模与分析

大展弦比柔性机翼结构重量轻、气动效率高,广泛应用于高空长航时无人机(UAVs)。飞行过程中,这类机翼在气动力作用下发生大变形,线性结构模型不再适用,需要建立考虑几何大变形的结构模型。采用牛顿力学方法推导了考虑结构几何非线性的机翼结构动力学模型,该方法推导过程简洁、物理意义明确,可以与Hodges基于哈密顿原理的推导方法相互补充,相互验证。为了能够更准确地求解大展弦比柔性机翼的非定常气动力,建立了能够考虑机翼三维效应且适用于机翼空间大变形的非定常气动力模型。基于建立的非线性结构模型和非定常气动力模型,采用松耦合方法建立了非线性气动弹性模型,并通过算例验证了气弹模型的准确性。研究结果表明,大展弦比柔性机翼颤振速度对来流迎角和机翼的展长均较为敏感;当来流速度大于颤振速度时,由于几何非线性,机翼振动并未发散而是形成稳定的极限环振荡(LCO);随着来流速度进一步增加,机翼再次穿过临界稳定点,由不稳定系统变为稳定系统,直到随着速度的增加系统再次达到临界稳定状态。

Aeroelastic modeling and analysis of wings considering geometric nonlinearity

Flexible wings with high aspect ratio are widely used in high-altitude and long-endurance Unmanned Aerial Vehi-cles (UAVs) because of low structural weight and high aerodynamic lift-to-drag ratio .This kind of wings experience large ge-ometric deformation in flight ,and the linear structure model based on small deformation hypothesis is no longer applicable . Therefore ,it is necessary to build the structure model which can simulate geometric nonlinearity .Based on the Newtonian method ,the dynamic equations for the geometric non-linear structure model are derived ,which can be mutually validated by and complemented with the method based on Hamilton's principle derived by Hodges .To simulate the aerodynamics of flexi-ble wings more precisely ,a model for three-dimensional unsteady aerodynamics ,which can consider large deformation of the wing ,is built .Based on the nonlinear structure model and the unsteady aerodynamic model ,the nonlinear aeroelastic model is built through loose coupling .The precision of the aeroelastic model is verified through tests .The results show that the flutter speed of flexible wings is sensitive to the free-stream angles of attack and span-wise length .When the free-stream speeds exceed the flutter speed ,the wing's vibrations are stable Limited Cycle Oscillations (LCO) rather than divergence . However ,as the free-stream speeds continues increasing ,the wing's vibrations converge again and the damping turned to be positive .