一种基于CR理论的大柔性机翼非线性气动弹性求解方法
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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。
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in inertial and stiffness characteristics,and dynamic aeroelastic features,the linear aeroelastic analysis method is no longer applicable.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.
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in inertial and stiffness characteristics,and dynamic aeroelastic features,the linear aeroelastic analysis method is no longer applicable.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.
引文
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[14]王伟,周洲,祝小平,等.考虑几何非线性效应的大柔性太阳能无人机静气动弹性分析[J].西北工业大学学报,2014,32(4):499-504.WANG Wei,ZHOU Zhou,ZHU Xiao-ping,et al.Static aeroelastic characteristics analysis of a very flexible solar powered UAV with geometrical nonlinear effect considered[J].Journal of Northwestern Polytechnical University,2014,32(4):499-504.
[15]Palacios R,Murua J,Cook R.Structural and aerodynamic models in nonlinear flight dynamics of very flexible aircraft[J].AIAA Journal,2010,48(11):2648-2659.
[16]吴国荣,颜桂云,陈福全.柔性梁大柔度动力响应分析的多体系统方法[J].振动与冲击,2007,26(3):87-89.WU Guo-rong,YAN Gui-yun,CHEN Fu-quan.Large deflection dynamic response analysis of flexible beams bi multibody system method[J].Journal of Vibration and Shock,2007,26(3):87-89.
[17]张健,向锦武.侧向随动力作用下大展弦比柔性机翼的稳定性[J].航空学报,2010,31(11):2115-2123.ZHANG Jian,XIANG Jin-wu.Stability of high-aspect-ratio fiexible wings loaded by a lateral follower force[J].Chinese Journal of Aeronautics,2010,31(11):2115-2123.
[18]Laxman V,Venkatesan C.Chaotic response of an airfoil due to aeroelastic coupling and dynamic stall[J].AIAA Jourmal,2007,45(1):271-280.
[2]Patil M J,Hodges D H,Cesnik C E S.Nonlinearaeroelasticity and flight dynamics of high-altitude long-endurance Aircraft[R].AIAA-99-1470.
[3]Patil M J,Hodges D H.Flightdynamics of highly flexible flying wings[J].Journal of Aircraft,2006,43(6):1790-1798.
[4]Patil M J,Hodges D J,Cesnik C E S.Limit cycle oscillations in high-aspect-ratio wings[J].Journal of Fluid and Structures,2001,15:107-132.
[5]Xie Chang-chuan,Yang Chao.Linearization methods of nonlinear aeroelastic stability for complete aircraft with high-aspect-ratio wings[J].Sci China Tech Sci,2011,54:403-411.
[6]Shams S,Sadr M H,Haddadpour H.An efficient method for nonlinear aeroelasticy of slender wings[J].Nonlinear Dynamics,2012,67:659-681.
[7]周凌远,李乔.基于UL法的CR列式三维梁单元计算方法[J].西南交通大学学报,2006,41(6):690-695.ZHOU Ling-yuan,LI Qiao.Updated lagrangian co-rotational formulation for geometrically nonlinear FE analysis of 3D beam element[J].Journal of Southwest Jiaotong Unoversity,2006,41(6):690-695.
[8]Belytschko T,Schwer L.Large displacement,transient analysis of space frames[J].International Journal for Numerical Methods in Engineering,1977,11:65-84.
[9]Crisfield M A.A consistent Co-rotational formulation for nonlinear,three-dimensional,beam element[J].Computer Methods In Applied Mechanics And Engineering,1990,81:131-150.
[10]Crisfield M A.Non-linear finite element analysis of solids and structures,Volume 2:Advanced topics[M].John Wiley&Sons,Chichester,New York,Weinheim,Brisbane,Singapore,Toronto,2000.
[11]Crisfield M A,Galvanetto U,JelenicéG.Dynamics of 3-D co-rotational beams[J].Computational Mechanics,1997,20:507-519.
[12]Ghosh S,Roy D.Consistent quaternion interpolation for objective finite element approximation of geometrically exact beams[J].Computer Methods In Applied Mechanics And Engineering,2008,198:555-571.
[13]Le T N,Battini J M,Hjiaj M.Dynamics of 3d beam elements in a corotational context:a comparative study of established and new formulation[J].Finite Elements in Analysis and Design,2012,61:97-111.
[14]王伟,周洲,祝小平,等.考虑几何非线性效应的大柔性太阳能无人机静气动弹性分析[J].西北工业大学学报,2014,32(4):499-504.WANG Wei,ZHOU Zhou,ZHU Xiao-ping,et al.Static aeroelastic characteristics analysis of a very flexible solar powered UAV with geometrical nonlinear effect considered[J].Journal of Northwestern Polytechnical University,2014,32(4):499-504.
[15]Palacios R,Murua J,Cook R.Structural and aerodynamic models in nonlinear flight dynamics of very flexible aircraft[J].AIAA Journal,2010,48(11):2648-2659.
[16]吴国荣,颜桂云,陈福全.柔性梁大柔度动力响应分析的多体系统方法[J].振动与冲击,2007,26(3):87-89.WU Guo-rong,YAN Gui-yun,CHEN Fu-quan.Large deflection dynamic response analysis of flexible beams bi multibody system method[J].Journal of Vibration and Shock,2007,26(3):87-89.
[17]张健,向锦武.侧向随动力作用下大展弦比柔性机翼的稳定性[J].航空学报,2010,31(11):2115-2123.ZHANG Jian,XIANG Jin-wu.Stability of high-aspect-ratio fiexible wings loaded by a lateral follower force[J].Chinese Journal of Aeronautics,2010,31(11):2115-2123.
[18]Laxman V,Venkatesan C.Chaotic response of an airfoil due to aeroelastic coupling and dynamic stall[J].AIAA Jourmal,2007,45(1):271-280.