结构振动的鲁棒可靠性

王晓军; 邱志平

结构振动的鲁棒可靠性

北京航空航天大学航空科学与工程学院, 北京 100083

基金项目: 国家自然科学基金资助项目(10172013);航空基金资助项目(01B51046)

详细信息

作者简介:
王晓军(1978-),男,陕西岐山人,博士生,xjwang@buaa.edu.cn.

中图分类号: O 327; TU 311.3
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- 被引次数: 0
出版历程
- 收稿日期: 2003-07-07
- 网络出版日期: 2003-11-30

Robust reliability of structural vibration

School of Aeronautics Science and Technology, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

摘要

摘要: 以传统的结构振动概率设计方法为基础,用区间集(超长方体)将不确定变量定量化,降低了传统的概率统计方法对统计特性的过分要求,通过区间参数摄动法得到固有频率所在的区间集,建立了激振力频率与结构固有频率干涉的非概率模型,给出了结构振动鲁棒可靠性准则.振动鲁棒可靠性的度量是通过结构避免发生共振所允许的不确定量的大小来体现的.结构所能承受的不确定度越大就越可靠,反之就不可靠,在数学模型上表现为激振力频率区间集与结构固有频率区间集的偏序关系.通过数值算例表明了所提出的结构振动非概率鲁棒可靠性准则的可行性.
- 结构振动 /
- 区间数学 /
- 鲁棒可靠性 /
- 不确定变量
Abstract: Based on the conventional probabilistic design methods of structural vibration, modeling uncertain variables as interval (hyper-rectangle), a non-probabilistic interference model between the exciting frequencies and the natural frequencies of a structure was established and a non-probabilistic method of reliability analysis was presented, called robust criterion of reliability of structural vibration. A measure of reliability developed here is the amount of the uncertainty structure can tolerate before occurring resonance. The larger the structure can tolerate the amount of uncertainty, the more reliable, vice versa. It can be described as the partial order relation between the hype-rectangles in mathematics. Numerical example illustrates the feasibility of the presented non-probabilistic robust reliability criterion.
- structural vibration /
- interval mathematics /
- robust reliability /
- uncertain variables

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参考文献(1)

[1] 王延荣, 田爱梅. 结构振动可靠性设计方法研究[J]. 航空动力学报, 2003, 18(2):191~194 Wang Yanrong, Tian Aimei. Research on reliability design method of structural vibration [J]. Journal of Aerospace Power, 2003, 18(2) :191~194(in Chinese)  [2] 史进渊, 林振坤, 龚汉声. 透平机械零件振动的可靠性设计[J]. 航空动力学报, 1995, 10(3):263-266 Shi Jinyuan, Lin Zhenkun, Gong Hansheng. Reliability design of turbine part vibration[J]. Journal of Aerospace Power, 1995, 10(3):263~266(in Chinese) [3] 欧阳德, 孔瑞莲, 宋兆泓. 叶片振动可靠性估计方法研究[J]. 航空动力学报, 1998, 13(2):161~164 Ouyang De, Kong Ruilian, Song Zhaohong. An assessment method for blade vibration relaibility[J]. Journal of Aerospace Power, 1998, 13(2):161~162(in Chinese) [4] Ben-Haim Y. A non-probabilistic concept of reliability[J]. Structural Safety, 1994, 14:227~245 [5] Ben-Haim Y. A non-probabilistic measure of reliability of linear systems based on expansion of convex models[J]. Structural Safety, 1995, 17:91~109 [6] Ben-Haim Y. Robust reliability of structures[J]. Advances in Applied Mechanics, 1997, 33:1~41 [7] Ben-Haim Y. Robust reliability in the mechanical sciences[M]. Berlin:Springer-Verlag,1996 [8] 邱志平, 陈山奇, 王晓军. 结构非概率鲁棒可靠性准则[J]. 计算力学学报,2003 (已录用正在出版) Qiu Zhiping, Chen Shanqi, Wang Xiaojun. Criterion for non-probabilistic robust reliability of structures[J]. Journal of Computational Mechanics, 2003(in Press)(in Chinese)  [9] Alefeld G, Herzberger J. Introductions to interval computations [M]. New York:Academic Press, 1983 [10] Moore R E. Methods and applications of interval analysis . London:Prenice-Hall,Inc, 1979 [11] 邱志平, 顾元宪. 结构固有频率区域两种摄动算法[J]. 非线性动力学学报, 1998, 5(1):9~15 Qiu Zhiping, Gu Yuanxian. Two pertubation algorithm for interval of structral natural frequency[J]. Journal of Nonlinear Dynamics, 1998, 5(1):9~15(in Chinese)

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