含模糊参数振动系统的Taylor级数展开法

邱志平; 刘正权

含模糊参数振动系统的Taylor级数展开法

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-中国工程物理研究院联合NSAF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 327; O 159
计量
- 文章访问数: 3725
- HTML全文浏览量: 274
- PDF下载量: 725
- 被引次数: 0
出版历程
- 收稿日期: 2004-10-13
- 网络出版日期: 2005-12-31

Taylor series expansion method for vibration system with fuzzy parameters

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

摘要

摘要: 为研究模糊参数约束条件下振动结构模糊有限元平衡方程特征值的问题,通过模糊集合理论中隶属度的性质,把振动结构的不确定模糊参量表示成区间形式,得到区间有限元平衡方程,利用所提Taylor级数展开法求解可以得到特征值所在的区间集.将α水平截集下得到的区间解,通过模糊分解定理构造出振动结构模糊有限元平衡方程的模糊解,从而可以得到模糊参数约束条件下振动结构的固有频率的变化范围,为结构的模糊可靠性评价奠定了基础.通过数值算例表明了所提方法的可行性.
- 泰勒展开 /
- 模糊集 /
- 模糊有限元 /
- 振动分析
Abstract: To study the eigenvalues problem of vibration structure with fuzzy parameters, the Taylor series expansion method was proposed. Based on the property of membership level, the uncertain fuzzy parameters were expressed in the interval forms, and accordingly the fuzzy finite element equilibrium equation could be expressed by interval finite element equilibrium equation. The Taylor series expansion method was used to compute the eigenvalues interval sets of interval finite element equilibrium equation for the purpose of calculating the eigenvalues variety range of vibration structure with fuzzy parameters. The fuzzy result sets of eigenvalues could be constructed by interval result sets gained from computing the interval finite element equilibrium equation under every α-level through fuzzy decompose theorem. Consequently the variety range of natural frequencies can be obtained concerning vibration structures with fuzzy parameters and establish the foundation for fuzzy reliability evaluation. A numerical example is considered to illuminate the practicability of the method presented.
- Taylor expansion /
- fuzzy sets /
- fuzzy finite element method /
- vibration analysis

HTML全文

参考文献(1)

[1] Elishakoff I. Essay on uncertainties in elastic and viscoelastic structures:from A. M. Freudenthal's criticisms to modern convex modeling[J]. Computers and Structures, 1995, 56(6):871~895 [2] Rao S S, Sawyer J P. A fuzzy element approach for the analysis of imprecisely-defined system[J]. AIAA, 1995, 33(12):2364~2370 [3] Chen L, Rao S S. Fuzzy finite-element approach for the vibration analysis of imprecisely-defined system[J]. Finite Elements in Analysis and Design, 1997, 27:69~83 [4] Valliappan S, Pham T. Fuzzy finite element analysis of a foundation on an elastic soil medium[J]. Int J Numer Anal Methods Geomech, 1993, 17(11):771~789 [5] Wang G Y, Ou J P. Theory of fuzzy random vibration with fuzzy parameters[J]. Fuzzy Sets and Systems, 1990, 36:103~112 [6] 郭书祥, 吕震宙, 冯立富. 模糊运算和模糊有限元静力控制方程的求解 . 应用数学和力学, 2002, 23(9):936~942 Guo Shuxiang, Lü Zhenzhou, Feng Lifu. Fuzzy arithmetic and solving of the static governing equations of fuzzy finite element method[J]. Applied Mathematics and Mechanics, 2002, 23(9):936~942(in Chinese) [7] 禹智涛, 吕恩琳, 王彩华. 结构模糊有限元平衡方程的一种解法[J]. 重庆大学学报(自然科学版), 1996, 19(1):53~58 Yu Zhitao, Lü Enlin, Wang Caihua. A method of solving the structural fuzzy[J]. Journal of Chongqing University (Natural Science Edition), 1996, 19(1):53~58 (in Chinese) [8] 邱志平. 不确定参数结构静力响应和特征值问题的区间分析方法 . 长春:吉林工业大学应用力学系, 1994 Qiu Zhiping. Interval analysis for static response and eigenvalues problem of structures with uncertain parameters . Changchun:Department of Applied Mechanics. Jilin University of Technology, 1994(in Chinese) [9] Qiu Z P, Wang X J. 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 [10] 邱志平, 王晓军, 马\ 一. 不确定结构复特征值问题的区间Taylor级数方法 . 固体力学会议论文集 . 北京,2003. 1~6 Qiu Zhiping, Wang Xiaojun, Ma Yi. Interval Taylor series method for complex eigenvalues of structures with uncertain parameters . Solid Mechanics Conference . Beijing,2003.1~6(in Chinese) [11] Zadeh L A. Fuzzy sets[J]. Information and Control, 1965, 8:338~353

施引文献

资源附件(0)

访问统计