基于Lanczos方法的结构动力学灵敏度分析  

Sensitivity Analysis Based on Lanczos Algorithm in Structural Dynamics

作　　者：李书[1] 王波[1] 胡继忠[1] 

机构地区：[1]北京航空航天大学飞机设计研究所,北京100083

出　　处：《应用数学和力学》2003年第1期83-88,共6页Applied Mathematics and Mechanics

摘　　要：利用数学理论得到结构动力学重特征值的灵敏度表达式 ,从而解决了奇异性问题·　然后 ,为降低计算工作量 ,基于Lanczos方法得到降阶的结构系统 ,从而得到降阶的灵敏度分析近似解·　用一个算例证明的方法正确性·The sensitivity calculating formulas in structural dynamics was developed by utilizing the mathematical theorem and new definitions of sensitivities. So the singularity problem of sensitivity with repeated eigenvalues is solved completely. To improve the computational efficient, the reduction system is obtained based on Lanczos vectors. After incorporating the mathematical theory with the Lanczos algorithm, the approximate sensitivity solution can be obtained. A numerical example is presented to illustrate the performance of the method.

关 键 词：结构动力学 灵敏度分析 有限元方法 特征值 特征向量 奇异性问题 LANCZOS方法 

分 类 号：TU311.3[建筑科学—结构工程] O241.6[理学—计算数学]