基于传递函数法的带多个外挂机翼颤振分析
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摘要
基于带外挂机翼结构和气动特点,使用带有半解析半数值特性的传递函数方法进行处理.首先,通过机翼的运动微分方程、二元机翼非定常气动力Therdorson模型、结合外挂挂载处的内力平衡与位移状态条件,得到了三维的带多个外挂大展弦比机翼的颤振微分方程.进而,使用传递函数方法,先将颤振计算方程整理成为状态空间方程形式,结合求解复特征值的方法,完成了带多个外挂大展弦比机翼的动气动弹性稳定性分析.对比已有文献的计算结果以及通过有限元方法进行的仿真结果,证实了文章所提计算方法的准确性和高效性,结合传递函数方法的优势,进一步将文章方法拓展到机翼的固有频率和发散速度求解.文章结尾,分析了外挂数量、外挂质量、转动惯量及位置分布等变量对带多个外挂大展弦比机翼的动气动弹性稳定性的影响.
The semi-analytical and semi-numerical transfer function method is applied to the flutter of a high-aspect-ratio aircraft wing with many concentrated external stores. Firstly, the flutter differential equation of a three-dimensional wing is established by combining the bend-twist vibration equations of the wing, the Therdorson unsteady aerodynamics model for the clean wings and the deformation harmony and internal force balance conditions on the position of the external store. Then, the control equations are formulated in a state-space form by defining a state vector by the transfer function method. Combined with the method of solving complex eigenvalues, both the flutter velocity and flutter frequency are obtained. The results are in good agreement with the literature solutions and the finite element method solutions, which proves that the present method is correct and efficient.Additionally, the torsion divergence and the natural frequency of the aircraft wing can be easily obtained by the transfer function method. Finally, the effects of quantity, the mass, the moment inertia and the position of the external stores are investigated.
The semi-analytical and semi-numerical transfer function method is applied to the flutter of a high-aspect-ratio aircraft wing with many concentrated external stores. Firstly, the flutter differential equation of a three-dimensional wing is established by combining the bend-twist vibration equations of the wing, the Therdorson unsteady aerodynamics model for the clean wings and the deformation harmony and internal force balance conditions on the position of the external store. Then, the control equations are formulated in a state-space form by defining a state vector by the transfer function method. Combined with the method of solving complex eigenvalues, both the flutter velocity and flutter frequency are obtained. The results are in good agreement with the literature solutions and the finite element method solutions, which proves that the present method is correct and efficient.Additionally, the torsion divergence and the natural frequency of the aircraft wing can be easily obtained by the transfer function method. Finally, the effects of quantity, the mass, the moment inertia and the position of the external stores are investigated.
引文
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[2]杨智春,赵令诚.带外挂二元机翼颤振模态的转变[J].航空学报,1992,13(9):A552-A554.
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[5]杨翊仁,赵令诚.二元机翼带外挂系统极限环颤振次谐响应分析[J].航空学报,1992,13(7):410-415.
[6]叶炜梁.带翼梢外挂的CKI机翼颤振分析[J].南京航空航天大学学报,1993,25(4):554-560.
[7]YANG Y R.KBM method of analyzing limit cycle flutter of a wing with an external store and comparison with a wind-tunnel test[J].Journal of Sound and Vibration,1995,187(2):271-280.
[8]KARPEL M,MOULIN B,ANGUITA L,et al.Flutter analysis of aircraft with external stores using modal coupling[J].Journal of Aircraft,2004,47(4):892-901.
[9]TANG D,DOWELL E H.Flutter and limit-cycle-oscillations for a wing-store model with freeplay[J].Journal of Aircraft,2006,43(2):487-503.
[10]LIBRESCU L,SONG O.Dynamics of composite aircraft wings carrying external stores[J].AIAA Journal,2008,46(3):568-578.
[11]FAZELZADEH S A,MARZOCCA P,RASHID E,et al.Effects of rolling maneuver on divergence and flutter of aircraft wing store[J].Journal of Aircraft,2010,47(1):64-71.
[12]周秋萍,邱志平.机翼带外挂系统极限环颤振的区间分析[J].航空学报,2010,31(3):514-518.
[13]OZCAN O,UNAL M F,ASLAN A R,et al.Aeroelastic chanracteristics of external store configurations at low speeds[J].Journal of Aircraft,2011,32(1):161-171.
[14]TANG D M,DOWELL E H.Aeroelastic analysis and experiment for wing/store model with stiction nonlinearity[J].Journal of Aircraft,2011,48(5):1512-1530.
[15]CHEN Y M,LIU J K,MENG G.An incremental method for limit cycle oscillations of an airfoil with an external store[J].International Journal of Non-Linear Mechanics,2012,47:75-83.
[16]许军,马晓平.带外挂机翼的极限环颤振分析[J].机械强度,2014,36(6):841-845.
[17]HAMID P,ABBAS M,AHMAD F S.Flutter analysis of an aircraft wing carrying,elastically,an external store[J].Applied Clay Science,2015,61(61):44-51.
[18]YANG Z,ZHAO L.Transition of the flutter mode of a two-dimensional section with an external store[J].Journal of Aircraft,2015,29(3):511-512.
[19]AMOOZGAR M,SHAHVERDI H.Investigation of adding fins to external stores for improving the flutter characteristics of a wing/store configuration[J].Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering,2016,230(8):201-205.
[20]段静波,江涛.带外挂机翼颤振分析的传递函数方法[J].振动与冲击,2017,36(10):109-116.
[21]ZAHRA S,HODGES D H,CHANG C S.Validation studies for aeroelastic trim and stability analysis of highly flexible aircraft[J].Journal of Aircraft,2010,47(4):1240-1247.
[22]赵永辉.气动弹性力学与控制[M].北京:科学出版社,2006,194-197.
[2]杨智春,赵令诚.带外挂二元机翼颤振模态的转变[J].航空学报,1992,13(9):A552-A554.
[3]杨智春,赵令诚,李伶,等.偏航、侧摆联接刚度对带外挂三角机翼颤振特性的影响[J].振动工程学报,1992,5(2):168-172.
[4]杨智春,赵令诚.联接刚度对机翼/外挂系统颤振边界特性的影响[J].应用力学学报,1993,10(2):1-6.
[5]杨翊仁,赵令诚.二元机翼带外挂系统极限环颤振次谐响应分析[J].航空学报,1992,13(7):410-415.
[6]叶炜梁.带翼梢外挂的CKI机翼颤振分析[J].南京航空航天大学学报,1993,25(4):554-560.
[7]YANG Y R.KBM method of analyzing limit cycle flutter of a wing with an external store and comparison with a wind-tunnel test[J].Journal of Sound and Vibration,1995,187(2):271-280.
[8]KARPEL M,MOULIN B,ANGUITA L,et al.Flutter analysis of aircraft with external stores using modal coupling[J].Journal of Aircraft,2004,47(4):892-901.
[9]TANG D,DOWELL E H.Flutter and limit-cycle-oscillations for a wing-store model with freeplay[J].Journal of Aircraft,2006,43(2):487-503.
[10]LIBRESCU L,SONG O.Dynamics of composite aircraft wings carrying external stores[J].AIAA Journal,2008,46(3):568-578.
[11]FAZELZADEH S A,MARZOCCA P,RASHID E,et al.Effects of rolling maneuver on divergence and flutter of aircraft wing store[J].Journal of Aircraft,2010,47(1):64-71.
[12]周秋萍,邱志平.机翼带外挂系统极限环颤振的区间分析[J].航空学报,2010,31(3):514-518.
[13]OZCAN O,UNAL M F,ASLAN A R,et al.Aeroelastic chanracteristics of external store configurations at low speeds[J].Journal of Aircraft,2011,32(1):161-171.
[14]TANG D M,DOWELL E H.Aeroelastic analysis and experiment for wing/store model with stiction nonlinearity[J].Journal of Aircraft,2011,48(5):1512-1530.
[15]CHEN Y M,LIU J K,MENG G.An incremental method for limit cycle oscillations of an airfoil with an external store[J].International Journal of Non-Linear Mechanics,2012,47:75-83.
[16]许军,马晓平.带外挂机翼的极限环颤振分析[J].机械强度,2014,36(6):841-845.
[17]HAMID P,ABBAS M,AHMAD F S.Flutter analysis of an aircraft wing carrying,elastically,an external store[J].Applied Clay Science,2015,61(61):44-51.
[18]YANG Z,ZHAO L.Transition of the flutter mode of a two-dimensional section with an external store[J].Journal of Aircraft,2015,29(3):511-512.
[19]AMOOZGAR M,SHAHVERDI H.Investigation of adding fins to external stores for improving the flutter characteristics of a wing/store configuration[J].Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering,2016,230(8):201-205.
[20]段静波,江涛.带外挂机翼颤振分析的传递函数方法[J].振动与冲击,2017,36(10):109-116.
[21]ZAHRA S,HODGES D H,CHANG C S.Validation studies for aeroelastic trim and stability analysis of highly flexible aircraft[J].Journal of Aircraft,2010,47(4):1240-1247.
[22]赵永辉.气动弹性力学与控制[M].北京:科学出版社,2006,194-197.