摘要
将不确定结构中的区间参数用泛灰数表示,对获得广义区间特征值方程的求解方法进行了研究,提出了一种简洁的算法。利用泛灰数的可扩展性对区间问题进行了分析,通过数学算例说明泛灰数不仅具有区间分析功能,且能解决区间分析所不能解决的问题。根据广义Rayleigh商的性质和对区间特征值的单调性分析,研究了广义区间特征值方程的求解方法,提出了一种基于泛灰数学的计算广义Rayleigh商法。将此算法应用于两个算例,通过与其他算法结果比较,验证了该方法具有计算简单、准确可靠,故有一定的工程应用价值。
Solution to a generalized interval eigenvalues equation is studied by denoting the interval parameters of uncertain structure with universal grey numbers,and a concise algorithm is presented.It is showed that universal grey mathematics can deal with some problems that interval analysis can′t by analysing interval problem with extensible characteristic of universal grey number.Then the solution to the interval eigenvalues equation is achieved with universal grey mathematics method,which is based on the characteristic of Rayleigh quotient and the monotonicity of interval eigenvalues.Finally,two examples are employed to show that this method is simple,accurate and reliable.
出处
《振动．测试与诊断》
EI
CSCD
北大核心
2013年第3期416-420,525,共5页
Journal of Vibration,Measurement & Diagnosis
基金
国家自然科学基金资助项目(50905134)
关键词
不确定结构
区间分析
固有频率
泛灰数学
RAYLEIGH商
uncertainty structure,interval analysis,natural frequency,universal grey mathematics,Rayleigh quotient
