多自由度强非线性颤振分析的增量谐波平衡法

蔡铭; 刘济科; 李军

多自由度强非线性颤振分析的增量谐波平衡法

1.
中山大学工学院, 广州 510275;2.中山大学应用力学与工程系,广州 510275

基金项目: 高等学校博士学科点专项科研基金资助项目(20050558032);广东省自然科学基金资助项目(05003295)

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作者简介:
蔡铭(1977- ),男,广东人,讲师,博士(Tel:+86-20-84112638;E-mail:eaiming@mail.sysu.edu.cn);刘济科(联系人.Tel:+86-20-84114666;Fax:+86-20-84039914;E-mail:jikeliu@hotmail.com).

中图分类号: O322；V215.3+4
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出版历程
- 收稿日期: 2004-10-10
- 修回日期: 2006-04-04
- 刊出日期: 2006-07-15

Incremental Harmonic Balance Method for Airfoil Flutter With Multiple Strong Nonlinearities

1.
School of Engineering, Zhongshan University, Guangzhou 510275, P. R. China;

摘要

摘要: 对多个自由度上含有强非线性项系统的颤振问题，推广应用增量谐波平衡法进行分析．考虑带有强非线性立方平移和俯仰刚度项的二元机翼颤振方程，首先将方程用矩阵形式表示，然后把振动过程分解成为振动瞬态的持续增量过程，再采用振幅作为控制参数应用谐波平衡法，以这种推广的增量谐波平衡法求得方程解的表达式，并由此分析系统的分岔现象、极限环颤振现象和谐波项数的取值问题，最后用龙格-库塔数值方法进行验算，结果表明：分析多个自由度的强非线性颤振，增量谐波平衡法是精确有效的．
- 强非线性颤振 /
- 增量谐波平衡法 /
- 分岔 /
- 极限环
Abstract: The incremental harmonic balance method was extended to analyze the flutter of systems with multiple structural strong nonlinearities. The strongly nonlinear cubic plunging and pitching stif-f ness terms were considered in the flutter equations of two-dimensional airfoil. First, the equations were transferred into matrix form, then the vibration process was divided into the persistent incremental processes of vibration moments. And the expression of their solutions could be obtained by using a certain amplitude as control parameter in the harmonic balance process, and then the bifurcation, limit cycle flutter phenomena and the number of harmonic terms were analyzed. Finally, numerical results calculated by the Runge-Kutta method were given to verify the results obtained by the proposed procedure. It has been shown that the incremental harmonic method is effective and precise in the analysis of strongly nonlinear flutter with multiple structural nonlinearities.
- strongly nonlinear flutter /
- incremental harmonic balance method /
- bifurcation /
- limit cycle

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参考文献(12)

[1]	Woolston D S,Runyan H L,Andrews R E. An investigation of effects of certain types of structural nonlinearities on wing and control surface flutter[J].Journal of the Aeronautical Sciences,1957,24(1):57—63.
[2]	Shen S F.An approximate analysis of nonlinear flutter problem[J].Journal of the Aeronautical Sciences,1959,28(1):25—32,45.
[3]	Breitbach E.Flutter Analysis of an Airplane With Multiple Structural Nonlinearities in the Control System[M]. Hampton, Virginia: National Aeronautics and Space Administration, NASA TN-1620,1980.
[4]	Liu J K,Zhao L C.Bifurcation analysis of airfoils in incompressible flow[J].Journal of Sound and Vibration,1992,154(1):117—124. doi: 10.1016/0022-460X(92)90407-O
[5]	Yang Y R,Zhao L C. Subharmonic bifurcation analysis of wing with store flutter[J].Journal of Sound and Vibration,1992,157(3):477—484. doi: 10.1016/0022-460X(92)90528-6
[6]	Lee C L.An iterative procedure for nonlinear analysis[J].American Institute of Aeronautics and Astronautics Journal,1986,24(5):833—840.
[7]	Lau S L,Cheung Y K.Amplitude incremental variational principle for nonlinear vibration of elastic system[J].ASME Journal of Applied Mechanics,1981,48(4):959—964. doi: 10.1115/1.3157762
[8]	Cheung Y K,Chen S H,Lau S L. Application of the incremental harmonic balance method to cubic non-linearity systems[J].Journal of Sound and Vibration,1990,140(2):273—286. doi: 10.1016/0022-460X(90)90528-8
[9]	Wong C W, Zhang W S, Lau S L. Periodic forced vibration of unsymmetrical piecewise linear systems by incremental harmonic balance method[J].Journal of Sound and Vibration,1991,149(1):91—105. doi: 10.1016/0022-460X(91)90913-5
[10]	Zhang W Y,Huseyin K.Complex formulation of the IHB technique and its comparison with other methods[J].Applied Mathematical Modelling,2001,26(1):53—75.
[11]	蔡铭,刘济科,杨怡.强非线性颤振分析的增量谐波平衡法[J].机械科学与技术,2004,23(6):742—744.
[12]	Zhao L C,Yang Z C.Chaotic motion of an airfoil with nonlinear stiffness in incompressible flow[J].Journal of Sound and Vibration,1990,138(2):245—254. doi: 10.1016/0022-460X(90)90541-7

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多自由度强非线性颤振分析的增量谐波平衡法

作者简介:
蔡铭(1977- ),男,广东人,讲师,博士(Tel:+86-20-84112638;E-mail:eaiming@mail.sysu.edu.cn);刘济科(联系人.Tel:+86-20-84114666;Fax:+86-20-84039914;E-mail:jikeliu@hotmail.com).

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Incremental Harmonic Balance Method for Airfoil Flutter With Multiple Strong Nonlinearities

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多自由度强非线性颤振分析的增量谐波平衡法

作者简介: 蔡铭(1977- ),男,广东人,讲师,博士(Tel:+86-20-84112638;E-mail:eaiming@mail.sysu.edu.cn);刘济科(联系人.Tel:+86-20-84114666;Fax:+86-20-84039914;E-mail:jikeliu@hotmail.com).

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出版历程

Incremental Harmonic Balance Method for Airfoil Flutter With Multiple Strong Nonlinearities

计量

出版历程

目录

作者简介:
蔡铭(1977- ),男,广东人,讲师,博士(Tel:+86-20-84112638;E-mail:eaiming@mail.sysu.edu.cn);刘济科(联系人.Tel:+86-20-84114666;Fax:+86-20-84039914;E-mail:jikeliu@hotmail.com).