复固有频率问题的模糊变分原理  

THE FUZZY VARIATIONAL PRINCIPLE OF COMPLEX NATURAL FREQUENCY

作　　者：邱志平[1] 张旭东[1] 

机构地区：[1]北京航空航天大学航空科学与工程学院,北京100191

出　　处：《固体力学学报》2015年第1期8-19,共12页Chinese Journal of Solid Mechanics

基　　金：高等学校学科创新引智计划(B07009);国家自然科学基金(11372025;11002013和11432002);航空科学基金(2012ZA51010);国防基础科研计划基金项目(JCKY2013601B)资助

摘　　要：模糊变分原理是模糊有限元重要的理论基础之一,模糊有限元的研究已经比较成熟了,然而关于模糊变分原理的研究却非常少.为研究复固有频率问题的模糊变分原理,首先介绍了一些模糊数学的概念,之后推导了非保守系统的拟Hamilton变分原理.接着通过将模糊参数引入到拟Hamilton变分原理,推导了复固有频率问题的模糊变分原理.作为模糊变分原理的应用,又推导了模糊有限元法.该方法可以直接得到问题的模糊解.与传统的模糊有限元方法相比,它避免了先将模糊参数转化为区间形式求解,之后再由区间解构造模糊解的过程.因此,该方法可以很大程度上减少计算量.最后通过数值算例表明了所提方法的可行性.The fuzzy variational principle（FVP）is one of the important theoretic bases of the fuzzy finite element method（FFEM）.Research works on fuzzy finite element method are relatively mature,however,research works on fuzzy variational principle are few.In order to study the fuzzy variational principle of complex natural frequency,firstly,some concepts of the fuzzy mathematics are introduced.And then,the quasi-Hamilton variational principle of non-conservative system is established.The fuzzy variational principle of complex natural frequency is derived by introducing fuzzy parameters into the quasi-Hamilton variational principle.After that,the fuzzy finite element method is presented as the application of the fuzzy variational principle.The presented method can obtain the fuzzy result directly.Compared with conventional fuzzy finite element methods,it avoids the case that the fuzzy parameters are transformed into interval parameters before calculation and then the fuzzy result is constructed by interval results.Therefore,the presented method can reduce the computational cost significantly.Finally,numerical examples are considered to illustrate the practicability of the presented method.

关 键 词：复固有频率 拟Hamilton变分原理 模糊变分原理 模糊有限元 

分 类 号：O159[理学—数学] O342[理学—基础数学]