考虑物理参数摄动的静气动弹性鲁棒分析

Robustness Analysis of Static Aeroelastic Systems with Physical Parameters Perturbation

为了研究静气动弹性系统在不确定性摄动下的稳定性和性能,建立了一种考虑物理参数摄动的静气动弹性鲁棒分析方法。从静气动弹性系统的物理方程出发,应用摄动理论和线性分式变换推导了由物理参数摄动引起的广义刚度、结构模态和广义定常气动力的摄动模型,然后得到了静气动弹性系统不确定性模型。将结构奇异值μ分析推广应用于静气动弹性鲁棒性分析。以一大展弦比长直机翼为例,分析了机翼前梁的材料弹性模态受到一定摄动时的鲁棒静发散稳定性和静气动弹性变形性能。数值结果验证了该方法是准确有效的。

To study the static aeroelastic stability and performances under the perturbation of uncertainties, a scheme for robustness analysis of static aeroelastic systems with physical parameters perturbation is developed. Based on the physical equations of static aeroelastic systems, the perturbation models of the generalized stiffness, the structural modes, and the generalized steady aerodynamics due to physical parameters perturbation are derived by using the perturbation theory and the linear fractional transformation. Then the static aeroelastic models with uncertainties are obtained. The structured singular value μ-analysis is expanded to analyzing the static aeroelastic robustness. The numerical application is performed for robust static divergence and aeroelastic deformation of a large aspect-ratio wing with perturbation on the elastic modulus of its fore-beam. The example shows the validity in robustness analysis of static aeroelastic systems by p-analysis.