A method based on an equivalent plate model for the dynamic and flutter analysis of a missile wing is developed. In the process of equivalent plate modeling, simple polynomials are used to describe the geometry, structure and displacement of the missile wing, and artificial springs are used to approximate the boundary conditions. The analytical expressions for the matrices of stiffness and mass are obtained by the global Ritz method. The natural frequencies and modes of the missile wing are obtained by solving the eigenvalue problem. Preliminary comparison between the frequencies and the modes from the new method and the finite element method indicates that the two methods are consistent. Then the two sets of modes are used to perform a flutter analysis and the results agree well, which further validates the accuracy of the equivalent plate method for analyzing the dynamic characteristics of a missile wing. The equivalent plate model provides an efficient tool for quick modeling of missile wings in the early design stage.
YANG Youxu, WU Zhigang, YANG Chao
. Flutter Analysis of Missile Wing Using Equivalent Plate Model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011
, 32(5)
: 833
-840
.
DOI: CNKI:11-1929/V.20101213.1757.008
[1] 陈桂彬, 邹丛青, 杨超. 气动弹性设计基础[M]. 北京: 北京航空航天大学出版社, 2004: 78-93. Chen Guibin, Zou Congqing, Yang Chao. Elements of aeroelastic dynamics[M]. Beijing: Beihang University Press, 2004: 78-93. (in Chinese)
[2] Kapania R K, Youhua L. Static and vibration analyses of general wing structures using equivalent-plate models[J]. AIAA Journal, 2000, 38(7): 1269-1277.
[3] 张旭. 基于等效梁方法的结构快速建模与气动弹性分析. 北京: 北京航空航天大学航空科学与工程学院, 2009. Zhang Xu. Fasting modeling and aeroelastic analysis based on the method of equivalent beam. Beijing: School of Aeronautic Science and Engineering, Beihang University, 2009. (in Chinese)
[4] Giles G L. Equivalent plate analysis of aircraft wing box structures with general planform geometry[J]. Journal of Aircraft, 1986, 23(11): 859-864.
[5] Giles G L. Further generalization of an equivalent plate representation for aircraft structural analysis[J]. Journal of Aircraft, 1989, 26(1): 67-74.
[6] Tizzi S. Numerical procedure for the dynamic analysis of three-dimensional aeronautical structures[J]. Journal of Aircraft, 1997, 34(1): 120-130.
[7] Tizzi S. Improvement of a numerical procedure for the dynamic analysis of aircraft structures[J]. Journal of Aircraft, 2000, 37(1): 144-154.
[8] Livne E. Equivalent plate structural modeling for wing shape optimization including transverse shear[J]. AIAA Journal, 1994, 32(6): 1278-1288.
[9] Livne E, Navarro I. Nonlinear equivalent plate modeling of wing-box structures[J]. Journal of Aircraft, 1999, 36(5): 851-865.
[10] Demasi L, Livne E. Structural Ritz-based simple-polynomial nonlinear equivalent plate approach: an assessment[J]. Journal of Aircraft, 2006, 43(6): 1685-1697.
[11] Kapania R K, Lovejoy A E. Free vibration of thick generally laminated cantilever quadrilateral plates[J]. AIAA Journal, 1996, 34(7): 1474-1486.
[12] Reissner E. The effect of transverse shear deformation on the bending of elastic plates[J]. Journal of Appplied Mechanics, 1945, 12: 69-77.
[13] Mindlin R D. Influence of rotatory interia and shear on flexural motions of isotropic, elastic plates[J]. Journal of Applied Machanics, 1951, 18: 31-38.
[14] Rodden W P, Harder R L, Bellinger E D. Aeroelastic addition to NASTRAN. NASA-CR-3094, 1979.
[15] Chen P C. Damping perturbation method for flutter solution: the g-method[J]. AIAA Journal, 2000, 38(9): 1519-1524.
[16] Chen P C, Liu D D. Unsteady supersonic computation of arbitrary wing-body configurations including external stores[J]. Journal of Aircraft, 1990, 27(2): 108-116.