复合材料层合梁自由振动的区间分析

邱志平; 邱薇; 王晓军

复合材料层合梁自由振动的区间分析

北京航空航天大学航空科学与工程学院, 北京 100083

基金项目: 航天支撑技术基金资助项目(20032.2BH03); 国家杰出青年科学基金资助项目(10425208); 国家自然科学基金委与中国工程物理研究院联合基金资助项目(10376002)

详细信息

作者简介:
邱志平(1962-),男,吉林长春人,教授, zpqiu@buaa.edu.cn.

中图分类号: O 324
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- 被引次数: 0
出版历程
- 收稿日期: 2005-07-22
- 网络出版日期: 2006-07-31

Interval analysis for free vibration of composite laminated beams

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

摘要

摘要: 利用区间数学研究了具有有界不确定结构参数的复合材料层合梁自由振动问题.将不确定结构参数用区间向量进行定量化,结合区间数学与Taylor级数,提出了求解具有不确定结构参数的复合材料层合梁自由振动问题的区间分析法.与传统的概率分析方法相比,它只需不确定参数所在范围的界限,而不需要其它任何概率统计信息来确定结构振动固有频率的变化区间.通过数值算例,将非概率区间分析法和概率分析方法进行了比较,可看出由区间分析方法得到的固有频率区间包含由概率方法得到的固有频率区间,即概率方法得到的区间宽度比区间分析方法得到的区间宽度要"紧",表明了区间分析方法的可行性和有效性.
- 复合材料 /
- 自由振动 /
- 不确定参数 /
- 区间分析
Abstract: A new method named interval analysis method, which solves the free vibration of composite laminated beams with uncertain parameters, was presented. Based on interval mathematics and Taylor series expansion, uncertain parameters were described by interval numbers. Instead of conventional probabilistic approach, interval analysis method could get the variation intervals of the natural frequencies of structure, in which the bounds on the magnitude of uncertain parameters were only required, not necessarily knowing other information of statistics. From the comparison between the non-probabilistic interval analysis method and the probabilistic approach in the numerical examples, it could be seen that the region of the natural frequency of structures with uncertain parameters obtained by the interval analysis method contained that produced by the probabilistic approach. In other words, the width of the maximum or upper and minimum or lower bounds on the natural frequency yielded by the probabilistic approach was tighter than that produced by the interval analysis method. The result illustrates the feasibility and the efficiency of the interval analysis method.
- composite materials /
- free vibration /
- uncertain parameters /
- interval analysis

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参考文献(1)

[1] Tewary V K.Mechanics of fiber composites[M].New York:Wiley,1978 [2] Kapania R K,Raciti S.Nonlinear vibrations of unsymmetrically laminated beams[J].AIAA Journal,1989,27(2):201-210 [3] Moore R E. Methods and applications of interval analysis[M].London:Prentice-Hall Inc,1979 [4] Alefeld G,Herzberger J.Introductions to interval computations[M].New York:Academic Press,1983 [5] Qiu Zhiping,Wang Xiaojun,Friswell M I. Eigenvalue bounds of structures with uncertain-but-bounded parameters[J].Journal of Sound and Vibration,2005,282(1-2):297-312 [6] Qiu Zhiping,Wang Xiaojun.Comparison of dynamic response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach[J].International Journal of Solids and Structures,2003,40(20):5423-5439 [7] 邱志平,马一,王晓军.含不确定参数的复合材料板振动的区间分析法[J].北京航空航天大学学报, 2004,30(7):682-685 Qiu Zhiping,Ma Yi,Wang Xiaojun. Interval analysis method for vibration of composite laminate with uncertain parameters[J].Journal of Beijing University of Aeronautics and Astronautics,2004,30(7):682-685(in Chinese) [8] 邱志平,王晓军,马一.结构复固有频率区域的区间摄动法[J].北京航空航天大学学报,2003,29(5):406-409 Qiu Zhiping,Wang Xiaojun,Ma Yi.Interval perturbation method for computing regions containing complex natural frequencies of structures[J].Journal of Beijing University of Aeronautics and Astronautics,2003,29(5):406-409(in Chinese) [9] 王晓军,邱志平.结构振动的鲁棒可靠性[J].北京航空航天大学学报,2003,29(11):1006-1010 Wang Xiaojun,Qiu Zhiping.Robust reliability of structural vibration[J].Journal of Beijing University of Aeronautics and Astronautics,2003,29(11):1006-1010(in Chinese) [10] 仝宗凯,王寿梅,邱志平.不确定初缺陷简支梁非线性屈曲载荷的确定[J].北京航空航天大学学报, 2000,26(4):424-427 Tong Zongkai,Wang Shoumei,Qiu Zhiping. Determination of non-linear buckling load for simple supported beam with bounded initial imperfection[J].Journal of Beijing University of Aeronautics and Astronautics,2000,26(4):424-427(in Chinese) [11] 仝宗凯,王寿梅,邱志平.用区间牛顿法跟踪结构的后屈曲路径[J].北京航空航天大学学报,2000,26(5):535-538 Tong Zongkai,Wang Shoumei,Qiu Zhiping. Application of nonlinear interval iteration method to post-buckling analysis of structures[J].Journal of Beijing University of Aeronautics and Astronautics,2000,26(5):535-538(in Chinese)

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