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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (12): 1475-.doi: https://doi.org/10.1007/s10483-009-1201-z

• Articles •    下一篇

Second-order sensitivity of eigenpairs in multiple parameter structures

陈塑寰1 郭睿2 孟广伟1   

  1. 1. College of Mechanical Science and Engineering, Nanling Campus, Jilin University, Changchun 130025, P. R. China;
    2. State Key Laboratory of Automobile Dynamic Simulation, Nanling Campus, Jilin University, Changchun 130025, P. R. China
  • 收稿日期:2009-02-17 修回日期:2009-10-12 出版日期:2009-12-23 发布日期:2009-12-01

Second-order sensitivity of eigenpairs in multiple parameter structures

CHEN Su-Huan1, GUO Rui2, MENG Guang-Wei1   

  1. 1. College of Mechanical Science and Engineering, Nanling Campus, Jilin University, Changchun 130025, P. R. China;
    2. State Key Laboratory of Automobile Dynamic Simulation, Nanling Campus, Jilin University, Changchun 130025, P. R. China
  • Received:2009-02-17 Revised:2009-10-12 Online:2009-12-23 Published:2009-12-01

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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.

关键词: multiple parameter structures, second-order sensitivity of eigenpairs, efficient computational method

Abstract: 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.

Key words: multiple parameter structures, second-order sensitivity of eigenpairs, efficient computational method

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