气动弹性研究中关于结构的分析通常采用柔度法和模态法。相比技术成熟、计算量大的柔度法，模态法具有阶次低、求解快和便于试验验证的优点。但其作为近似的分析方法，在工程应用中需要一定的经验，尚缺乏模态选取的准则，研究旨在为模态法的工程应用提供模态选取的定量评价标准。针对某典型飞行器进行升降舵效率、副翼效率等弹性修正分析，提出模态影响系数的概念来评估模态的选取对这些气动弹性分析的影响，并对结果加以解释。结果表明，模态影响系数指标合理，能够反映模态选取对气动弹性特性的影响，可以作为模态法中模态选取的定量评价指标。
The flexibility method and modal approach are usually used in structural analysis in the aeroelastic research. Compared to the flexibility method which is mature but brings higher computational cost for the solution，the modal approach has the advantage of significant reduction in the dimension of the problem，high efficiency and convenient for verification. However, there are no principles for the selection of modes and one must have enough engineering experience to fully utilize the modal approach in practice. To provide modal approach with its own quantitative criteria in practice, this paper first proposes the idea of modal influence coefficient to evaluate the effect of modal selection on modal approach of aeroelastic analysis. In order to validate the rationality and validity of the modal influence coefficient, the paper carrys out control efficiency and aeroelastic correction analysis for a typical aircraft. The results show that the modal influence coefficient can accurately evaluate the effect of modal selection on aeroelastic analysis, thus providing some helpful reference in practice.
[1] Chen G B, Yang C, Zou C Q. Fundamentals of Aeroelasticity(Second Edition)[M]. Beijing:Beijing University of Aeronautics and Astronautics Press, 2010. (in Chinese)
陈桂彬，杨超，邹从青.气动弹性设计基础（第2版）[M].北京：北京航空航天大学出版社，2010.
[2] Yang C, Wu Z G, Wan Z Q, et al. Principle of Aircraft Aeroelasticity[M]. Beijing: Beijing University of Aeronautics and Astronautics Press, 2011. (in Chinese)
杨超, 吴志刚, 万志强, 等. 飞行器气动弹性原理[M]. 北京：北京航空航天大学出版社，2011.
[3] Chen D W, Yang G W. Static aeroelastic analysis of flying-wing using different models[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(4): 469-479.(in Chinese)
陈大伟，杨国伟.静气动弹性计算方法研究[J].力学学报, 2009, 41(4): 469-479.
[4] Su W H, Cesnik C E S. Strain-Based Analysis for Geometrically Nonlinear Beams: A Modal Ap-proach[C]. The 53rd AIAA/ASME/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Ho-nolulu, HI, 2012-1713.
[5] Shi X M, Xu Q, YanG B Y, et al. Dynamics Modeling of Plane Symmetrical Vehicle Structural Based on Branch Mode Method[J]. AEROSPACE SHANGHAI, 2011, 28(2): 27-31.
史晓鸣, 许泉, 杨炳渊，等. 基于分支模态法的面对称布局飞行器结构动力学建模[J].上海航天，2011,28(2): 27-31.
[6] Wan Z Q, Tang C H, Yang C. Consistence analysis and validation of three methods for static aeroelastic di-vergence[J]. Acta Aeronautica et Astronautica Sinica, 2002, 23(4): 342-345. (in Chinese)
万志强,唐长红,杨超. 三种静气动弹性发散方法的一致性分析和验证[J].航空学报,2002,23(4):342-345.
[7] Yan D, Yang C, Wan Z Q. Static Aeroelastic Diver-gence Analysis by Introducing Correction Techniques of Aerodynamic Data[J]. Journal of Beijing University of Aeronautics and Astronautics, 2007, 33(10): 1146-1149.(in Chinese)
严德, 杨超, 万志强. 应用气动力修正技术的静气动弹性发散计算[J]. 北京航空航天大学学报, 2007, 33(10):1146-1149.
[8] ZAERO Theoretical Manual[M]. ZONA Technology, Inc.Fifteenth Edition, 2006.
[9] MSC.Nastran Aeroelastic Analysis User’s Guide[M]. MSC.Software Corporation, Version 68,2004.
[10] Yin H T, Jiang J H, Zhang F, et al. Finite Element Modeling Based on Experimental Modal Parameters and Structural Dynamics Optimization[J].Foreign Electronic Measurement Technology, 2012, 31(9): 18-22. (in Chinese)
殷海涛, 姜金辉, 张方, 沈敏. 基于试验模态参数及结构动力学优化设计的有限元建模[J]. 外国电子测量技术, 2012, 31(9): 18-22.
[11] Yang C, Zhang B C, Wan Z Q, et al. A Method for static aeroelastic analysis based on the high-order panel method and modal method[J]. Science China Technological Sciences, 2011, 54(3): 741-748.
[12] Jiang J H, Zhang F, Zhang M. Teaching Demonstra-tion System of Experiment Modal Parameter Identifi-cation Based on Virtual Instrument Technolo-gy[J].Foreign Electronic Measurement Technology, 2012, 31(2): 94-98. (in Chinese)
姜金辉, 张方, 张茅争. 基于虚拟仪器技术的模态参数识别教学演示系统[J]. 国外电子测量技术, 2012, 31(2): 94-98.
[13] Ward H, Stephen L, Bohr S. Modal Analysis Theory and Experiment[M]. Bai H T, Guo J Z, translated. Beijing Institute of Technology Press, 2001. (in Chi-nese)
沃德?海伦，斯蒂芬?拉门兹，波尔?萨斯.模态分析理论与试验[M]. 北京:北京理工大学出版社，2001.
[14] Cao S Q, Zhang D W, Xiao L X. Vibrational Structure Modal Analysis: Theoretical, Practice, and Appli-cation[M]. Tianjin:Tianjin University Press, 2001. (in Chinese)
曹树谦，张文德，萧龙翔. 振动结构模态分析：理论、实践与应用[M]. 天津:天津大学出版社，2001.
[15] Xia S L, Zhao L X, Tang K B, et al. The Investigation and Application of the Technique of CFD Simulation to Static Aeroelasticity Correction[C]. Xi’an: Northwes-tern Polytechnic University Press, 2009.
夏生林, 赵利霞, 唐克兵, 等. CFD技术在静气动弹性修正计算中的研究与应用[C]. 西安:西北工业大学出版社, 2009.
CJA