CO-ROTATIONAL APPROACH OF SOLVING NONLINEAR AEROELASTICY  OF VERY FLEXIBLE WINGS

WANG Wei 1,ZHOU Zhou 1,ZHU Xiao-ping 2,WANG Rui 1

Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (19) : 62-70.

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (19) : 62-70.

CO-ROTATIONAL APPROACH OF SOLVING NONLINEAR AEROELASTICY  OF VERY FLEXIBLE WINGS

  •   WANG Wei 1,ZHOU Zhou 1,ZHU Xiao-ping 2,WANG Rui 1 
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Abstract

Very flexible wings under aerodynamic loads tend to produce large deformation, which result in significant changes in inertial and stiffness characteristics as well as in dynamic aeroelastic response, and the linear aeroelastic model no longer applicable. Based on co-rotational(CR) theory, the tangent stiff matrix and mass matrix are derived, and the dynamical equilibrium equations of geometrically nonlinear structures of space beam elements are established in this paper. Coupling ONERA dynamic stall model, an efficient method of solving nonlinear aeroelasticy of very flexible wings is proposed. Using newmark direct integration method and loose coupled algorithms, a numerical procedure for solving nonlinear aeroelastic governing equations is presented, and the efficiency and precision of the method was proved through a test case. The results and their analysis show preliminary that: structural and aerodynamic nonlinearities should be considered for complete nonlinear dynamic aeroelastic simulations of very flexible wings; the critical limit cycle oscillation speed will decreases by 15% or more due to bending deformation of the wing, but will improved by translating elastic axis; the proposed method of solving nonlinear aeroelastic problems show a good precision and efficiency, and satisfied requirements of nonlinear aeroelastic analysis of very flexible wings.

Key words

nonlinear aeroelasticity / limit cycle oscillation / CR theory / unsteady aerodynamics / dynamic stall / newmark integration method

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WANG Wei 1,ZHOU Zhou 1,ZHU Xiao-ping 2,WANG Rui 1 . CO-ROTATIONAL APPROACH OF SOLVING NONLINEAR AEROELASTICY  OF VERY FLEXIBLE WINGS[J]. Journal of Vibration and Shock, 2015, 34(19): 62-70

References

[1] M.J. Patil, D.H. Hodges. On the importance of aerodynamic and structural geometrical nonlinearities in aeroelastic behavior of high-aspect-ration wings[J].Journal of Fluids and Structures,2004,19:905-915.
[2] M.J. Patil, D.H. Hodges, C E.S Cesnik. Nonlinear aeroelasticity and flight dynamics of high-altitude long-endurance aircraft [R]. AIAA-99-1470.
[3] M.J. Patil, D.H. Hodges. Flight dynamics of Highly Flexible Flying wings [J]. Journal of aircraft,2006,43(6):1790-1798.
[4] M.J.Patil, D.H.Hodges, C.E.S.Cesnik. 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] S.Shams, M.H.Sadr, H.Haddadpour.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 Lingyuan, 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(in chinese).
[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 MA. A consistent Co-rotational formulation for non-linear, three-dimensional, beam element[J]. Computer Methods In Applied Mechanics And Engineering, 1990,81:131-150.
[10] Crisfield MA. 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 MA, Galvanetto U, Jelenić G. 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 TN, Battini JM, 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 Xiaoping,Wang Rui. 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 (in Chinese)
[15] Rafael Palacios, Joseba Murua, Robert Cook. 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 Guorong,Yan Guiyun,Chen Fuquan.Large deflection dynamic response analysis of flexible beams bi multibody system method[J].Journal of vibration and shock, 2007,26(3):87-89(in chinese).
[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.
[18] V.Laxman,C.Venkatesan.Chaotic response of an airfoil due to aeroelastic coupling and dynamic stall[J].AIAA Jourmal, 2007,45(1):271-280.
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