Second-order sensitivity of eigenpairs in multiple parameter structures

• Published in: Applied mathematics and mechanics Vol. 30; no. 12; pp. 1475 - 1487
• Main Author: 陈塑寰 郭睿 孟广伟
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University Press 01.12.2009; College of Mechanical Science and Engineering, Nanling Campus, Jilin University,Changchun 130025, P. R. China%State Key Laboratory of Automobile Dynamic Simulation, Nanling Campus, Jilin University,Changchun 130025, P. R. China
• Subjects: Applications of Mathematics; Classical Mechanics; Computation; Eigenvalues; Eigenvectors; Fluid- and Aerodynamics; Hessian矩阵; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Matrices; Matrix methods; Partial Differential Equations; Perturbation methods; 二阶摄动; 参数结构; 敏感性; 灵敏度矩阵; 特征对; 第二特征值; efficient computational method; second-order sensitivity of eigenpairs; 45C05; multiple parameter structures; O327
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-009-1201-z

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.