Nonlinear dynamic characteristics of a folding fin with freeplay nonlinearities are analyzed based on the mode synthesis method. Firstly, the finite element model with hinge connection is established according to the structural characteristics of the folding fin, and subsequently reduced by using the free-interface mode synthesis method. Secondly, sweeping and modal tests are carried out on the folding fin without freeplay nonlinearities to test the accuracy of the finite element model and its reduced substructure model, and the equivalent linear joint stiffness of the hinge is obtained based on the model updating. Finally, the equivalent linear joint stiffness and the freeplay value are combined to obtain the nonlinear joint stiffness of the hinge under different freeplay, and the nonlinear dynamic model of the folding fin with freeplay nonlinearities is established. Numerical simulation of the folding fin with freeplay nonlinearities is carried out based on the nonlinear dynamic model, and the calculated results are in good agreement with their experimental counterparts, which further demonstrate the accuracy of the established nonlinear dynamic model and its feasibility in the analysis of nonlinear dynamic characteristics of folding fins.
[1] DOWELL E H, TANG D. Nonlinear aeroelasticity and unsteady aerodynamics[J]. AIAA Journal, 2002, 40(9):1697-1707.
[2] 丁千,陈予恕. 机翼颤振的非线性动力学和控制研究[J]. 科技导报, 2009, 27(2):53-61. DING Q, CHEN Y S. Non-linear dynamic and control of flutter of airfoil[J]. Science and Technology Review, 2009, 27(2):53-61(in Chinese).
[3] 刘芳,丁千. 含间隙折叠舵面的主共振响应分析[J]. 航空动力学报, 2016, 31(12):2965-2971. LIU F, DING Q. Primary resonance response analysis on folding rudder with gaps[J]. Journal of Aerospace Power, 2016, 31(12):2965-2971(in Chinese).
[4] 赵永辉,胡海岩. 具有操纵面间隙非线性二维翼段的气动弹性分析[J]. 航空学报, 2003, 24(6):521-525. ZHAO Y H, HU H Y. Aeroelastic analysis of a two-dimensional airfoil with control surface freeplay nonlinearity[J]. Acta Aeronautica et Astronautica Sinica, 2003, 24(6):521-525(in Chinese).
[5] GOLD P, KARPEL M. Reduced-size aeroservoelastic modeling and limit-cycle-oscillation simulations with structurally nonlinear actuators[J]. Journal of Aircraft, 2008, 45(2):471-477.
[6] BEHAL A, RAO D. Adaptive control for a nonlinear wing section with multiple flaps[J]. Journal of Guidance, Control and Dynamics, 2006, 29(3):744-750.
[7] 迟圣威. 折叠翼颤振理论分析和计算方法[D]. 南京:南京航空航天大学, 2011:11-17. CHI S W. Theoretical and computational flutter study for folding wing configuration[D]. Nanjing:Nanjing University of Aeronautics and Astronautics, 2011:11-17(in Chinese).
[8] ABDELKEFI A, VASCONCELLOS R, MARQUES F D, et al. Modeling and identification of freeplay nonlinearity[J]. Journal of Sound and Vibration, 2012, 331(8):1898-1907.
[9] 向树红,邱吉宝,王大钧. 模态分析与动态子结构方法新进展[J]. 力学进展, 2004, 34(3):289-303. XIANG S H, QIU J B, WANG D J. The resent progresses on modal analysis and dynamic sub-structure methods[J]. Advances in Mechanics, 2004, 34(3):289-303(in Chinese).
[10] KIM D, BAE J, LEE I, et al. Dynamic model establishment of a deployable missile control fin with nonlinear hinge[J]. Journal of Spacecraft and Rockets, 2005, 42(1):66-77.
[11] BAE J, KIM D, SHIN W, et al. Nonlinear aeroelastic analysis of a deployable missile control fin[J]. Journal of Spacecraft and Rockets, 2004, 41(2):264-271.
[12] 全炜倬,方明霞. 超音速飞行器翼——身组合体的颤振研究[J]. 噪声与振动控制, 2010, 30(6):1-4. QUAN W Z, FANG M X. Flutter study of wing-fuselage combination of supersonic aircrafts[J]. Noise and Vibration Control, 2010, 30(6):1-4(in Chinese).
[13] 倪迎鸽,侯赤,万小朋,等. 具有结构非线性的折叠机翼气动弹性分析[J]. 振动与冲击, 2016, 35(18):165-171. NI Y G, HOU C, WAN X P, et al. Aeroelastic analysis of a folding wing with structural nonlinearities[J]. Journal of Vibration and Shock, 2016, 35(18):165-171(in Chinese).
[14] 杨宁,吴志刚,杨超,等. 折叠翼的结构非线性颤振分析[J]. 工程力学, 2012, 29(2):197-204. YANG N, WU Z G, YANG C, et al. Flutter analysis of a folding wing with structural nonlinearity[J]. Engineering Mechanics, 2012, 29(2):197-204(in Chinese).
[15] YANG N, WANG N, ZHANG X, et al. Nonlinear flutter wind tunnel test and numerical analysis of folding fins with freeplay nonlinearities[J]. Chinese Journal of Aeronautics, 2016, 29(1):144-159.
[16] WU Z G, YANG N, YANG C. Identification of nonlinear multi-degree-of freedom structures based on Hilbert transformation[J]. Science China Physics, Mechanics & Astronomy, 2014, 57(9):1725-1736.
[17] WU Z G, YANG N, YANG C. Identification of nonlinear structures by the conditioned reverse path method[J]. Journal of Aircraft, 2015, 52(2):373-386.
[18] 胡海岩,赵永辉,黄锐. 飞机结构气动弹性分析与控制研究[J]. 力学学报, 2016, 48(1):1-27. HU H Y, ZHAO Y H, HUANG R. Studies on aeroelastic analysis and control of aircraft structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1):1-27(in Chinese).
[19] 王文亮,杜作润,陈康元. 模态综合技术短评和一种新的改进[J]. 航空学报, 1979(3):32-51. WANG W L, DU Z R, CHEN K Y. A short commentary for modal synthesis techniques and a novel improvement[J]. Acta Aeronautica et Astronautica Sinica, 1979(3):32-51(in Chinese).
[20] 王永岩. 动态子结构方法理论及应用[M]. 北京:科学出版社, 1999. WANG Y Y. Theory and application of dynamic substructure method[M].Beijing:Science Press,1999(in Chinese).
[21] RUBIN S. Improved component-mode representation for structural dynamic analysis[J]. AIAA Journal, 1975, 13(8):995-1006.
[22] 应祖光,邱吉宝,潭志勇. 精确剩余模态及其综合技术[J]. 振动工程学报, 1996, 9(1):38-46. YING Z G, QIU J B, TAN Z Y. Exact residual modes and their synthesis techniques[J]. Journal of Vibration Engineering, 1996, 9(1):38-46(in Chinese).
[23] NOL J P, KERSCHEN G. Nonlinear system identification in structural dynamics:10 more years of progress[J]. Mechanical Systems and Signal Processing, 2017, 83(15):2-35.
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