基于Taylor展式的不确定结构复特征值问题两种非概率方法比较研究

代替传统的处理不确定问题的概率统计方法，将利用区问数学和凸模型理论研究具有有界不确定参数的非比例阻尼结构复特征值所在区域问题．区间数学将有界不确定结构参数用超长方体即区问向量进行定量化，而凸模型理论则用椭球对有界不确定参数进行定量化．在不用知道不确定变量的概率统计特性的条件下，区间分析方法和凸模型理论都可以确定出有界不确定结构参数的非比例阻尼结构复特征值所在区域．通过数学证明和数值算例来说明，在凸模型理论中的椭球在由区间分析中的超长方体—区间向量来确定的条件下，由区间数学所确定出不确定结构复特征值实部和虚部的宽度要比凸模型所确定出的范围的宽度要小，而这正是工程技术人员所要求的结果。

COMPARISON OF TWO NONPROBABILISTIC METHODS FOR THE COMPLEX EIGENVALUE PROBLEM OF STRUCTURES WITH UNCERTAIN PARAMETERS

Instead of the conventional probabilistic statistical methods dealing with uncertain problems, interval mathematics and convex models are used to study, the problem on regions containing complex eigenvalues for non-proportional damping structures with uncertain but bounded parameters. Structural parameters with uncertain but bounded parameters are described by a hypercube-an interval vector in interval mathematics and by ellipsoid in convex models. Thus, not necessarily knowing the probabilistic distribution densities, the interval analysis method and convex models are used to compute complex interval eigenvalues of the generalized interval eigenvalue problem. By means of the mathematical proof and numerical examples, we can see that the width of the region on the dynamical response produced by the interval analysis method is smaller than that yielded by convex models.