一种基于CR理论的大柔性机翼非线性气动弹性求解方法

王伟1，周洲1，祝小平2，王睿1

(1.西北工业大学航空学院，西安710072；2. 西北工业大学无人机研究所，西安710065)

摘要：大展弦比大柔性机翼在气动载荷的作用下，产生较大的弹性变形，其惯性特性、刚度特性、动气动弹性特性等亦发生较大改变，常规的线性气动弹性分析方法不再适用。基于Co-rotational(CR)理论，推导了机翼变形后的切线刚度矩阵和质量矩阵，建立了考虑几何非线性效应的大柔性机翼结构动力学模型；耦合改进的ONERA非线性非定常气动力模型，提出了一种适用于大柔性机翼的非线性气动弹性求解方法。采用Newmark直接数值积分法及松耦合技术在时域内对气动弹性运动方程进行求解，对所提出的非线性气动弹性求解方法的正确性和精度进行了验证，并研究了大柔性机翼的极限环颤振特性。研究表明：适用于大柔性机翼完整的非线性气动弹性建模需要考虑机翼结构大变形和非定常气动力动态失速等非线性因素；弯曲变形可降低临界极限环颤振速度的15%以上，而前移弹性轴能够有效的提高临界极限环颤振速度；所提出的非线性气动弹性求解方法具有较好的精度和效率，满足大柔性机翼非线性气动弹性的求解需求。

关键词：非线性气动弹性；极限环颤振；CR理论；非定常气动力；动态失速；Newmark积分法

中图分类号:V211.47

文献标志码：A

DOI:10.13465/j.cnki.jvs.2015.19.010

Abstract:Very flexible wings under aerodynamic loads tend to produce larger deformation, it results in significant changes in inertial and stiffness characteristics, and dynamic aeroelastic features, the linear aeroelastic analysis method is no longer applicable. Here, based on the co-rotational(CR) theory, the tangent stiffness matrix and mass matrix of a wing after deformation were derived, the structural dynamic model of very flexible wings considering geometric nonlinearity was then established. Coupled with ONERA dynamic stall model, an efficient method to solve nonlinear aeroelasticity of very flexible wings was proposed. Using Newmark direct integration method and loose coupled algorithms, a numerical procedure for solving nonlinear aeroelastic dynamic equations was presented, and the efficiency and precision of the method were verified through tests. The results showed that structural and aerodynamic nonlinearities should be considered for complete nonlinear dynamic aeroelastic simulations of very flexible wings; the wing’s critical limit cycle oscillation speed decreases 15% or more due to its bending deformation, but it increases through shifting forward the wing’s elastic axis; the proposed method has a good precision and efficiency, and meets requirements of nonlinear aeroelastic analysis of very flexible wings.

基金项目：国家自然科学基金(51475387)

收稿日期：2014-06-12修改稿收到日期：2014-09-30

A CR theory-based approach for solving nonlinear aeroelasticity of very flexible wings

WANGWei1,ZHOUZhou1,ZHUXiao-ping2,WANGRui1(1. College of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China；2. UAV Research Institute, Northwestern Polytechnical University, Xi’an 710065, China)

Key words:nonlinear aeroelasticity; limit cycle oscillation; CR theory; unsteady aerodynamics loads; dynamic stall; Newmark integration method

高空超长航……