北京航空航天大学学报 ›› 2014, Vol. 40 ›› Issue (12): 1773-1779.doi: 10.13700/j.bh.1001-5965.2013.0749

• 论文 • 上一篇    下一篇

模糊变分原理在求解结构固有频率中的应用

张旭东, 邱志平, 李琦   

  1. 北京航空航天大学 航空科学与工程学院, 北京 100191
  • 收稿日期:2014-01-08 出版日期:2014-12-20 发布日期:2014-12-30
  • 作者简介:张旭东(1989-),男,河北唐山人,硕士生,tjuzxd@126.com.
  • 基金资助:

    高等学校学科创新引智计划资助项目(B07009);国家自然科学基金资助项目(11372025,11002013);航空科学基金资助项目(2012ZA51010);国防基础科研计划基金资助项目(JCKY2013601B)

Application of fuzzy variational principle in solution of natural frequency of structures

Zhang Xudong, Qiu Zhiping, Li Qi   

  1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2014-01-08 Online:2014-12-20 Published:2014-12-30

摘要:

在处理含模糊参数的结构固有频率问题时,现有的方法局限于先将模糊参数转化为区间数求解,再由区间解构造出相应的模糊解.由于现有方法计算量较大,所以提出了基于模糊变分原理的模糊里兹法和模糊有限元法.通过在瑞利商变分中直接引入模糊参数,得到了结构固有频率问题的模糊变分原理.作为模糊变分原理的应用,推导了模糊里兹法和模糊有限元法.这两种方法都可以直接得到问题的模糊解,与传统的区间解法相比,提高了计算效率.算例表明,这两种方法不但具有较高的计算精度,而且可以很大程度上减少计算量.

关键词: 模糊, 变分原理, 里兹法, 有限元法, 固有频率

Abstract:

When dealing with the natural frequency of structures with fuzzy parameters, the previous methods are limited to the case that the fuzzy parameters are transformed into the interval parameters before the calculation, and then the fuzzy results are constructed by the interval results. The calculation cost of the previous methods is relatively expensive, so the fuzzy Ritz method and the fuzzy finite element method which are based on the fuzzy variational principle were adopted. By introducing the fuzzy parameters into Rayleigh quotient variation, the fuzzy variational principle was developed. The fuzzy Ritz method and the fuzzy finite element method were proposed as the application of the fuzzy variational principle. These two methods can obtain the fuzzy result directly. Compared with the traditional interval analysis methods, the proposed methods can increase computational efficiency. The numerical example demonstrates that both methods can achieve high computational accuracy and reduce computational cost significantly.

Key words: fuzzy, variational principle, Ritz method, finite element method, natural frequency

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