Second-order sensitivity of eigenpairs in multiple parameter structures  

作　　者：陈塑寰 郭睿 孟广伟 

机构地区：[1]College of Mechanical Science and Engineering,Nanling Campus,Jilin University [2]State Key Laboratory of Automobile Dynamic Simulation,Nanling Campus,Jilin University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2009年第12期1475-1487,共13页应用数学和力学（英文版）

基　　金：Project supported by the 985-Engineering Innovation of Graduate Students of Jilin University;the Science and Technology Development Foundation of Jilin Province(20070541)

摘　　要：This paper presents methods for computing a second-order sensitivity matrix and the Hessian matrix of eigenvalues and eigenvectors of multiple parameter structures. Second-order perturbations of eigenvalues and eigenvectors are transformed into multiple parameter forms,and the second-order perturbation sensitivity matrices of eigenvalues and eigenvectors are developed.With these formulations,the efficient methods based on the second-order Taylor expansion and second-order perturbation are obtained to estimate changes of eigenvalues and eigenvectors when the design parameters are changed. The presented method avoids direct differential operation,and thus reduces difficulty for computing the second-order sensitivity matrices of eigenpairs.A numerical example is given to demonstrate application and accuracy of the proposed method.This paper presents methods for computing a second-order sensitivity matrix and the Hessian matrix of eigenvalues and eigenvectors of multiple parameter structures. Second-order perturbations of eigenvalues and eigenvectors are transformed into multiple parameter forms,and the second-order perturbation sensitivity matrices of eigenvalues and eigenvectors are developed.With these formulations,the efficient methods based on the second-order Taylor expansion and second-order perturbation are obtained to estimate changes of eigenvalues and eigenvectors when the design parameters are changed. The presented method avoids direct differential operation,and thus reduces difficulty for computing the second-order sensitivity matrices of eigenpairs.A numerical example is given to demonstrate application and accuracy of the proposed method.

关 键 词：multiple parameter structures second-order sensitivity of eigenpairs efficient computational method 

分 类 号：O151.21[理学—数学] TH132.46[理学—基础数学]