Second-Order Sensitivity of Eigenpairs of Multiple Parameter Structures

CHEN Su-huan; GUO Rui; MENG Guang-wei

doi:10.3879/j.issn.1000-0887.2009.12.001

Volume 30 Issue 12

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CHEN Su-huan, GUO Rui, MENG Guang-wei. Second-Order Sensitivity of Eigenpairs of Multiple Parameter Structures[J]. Applied Mathematics and Mechanics, 2009, 30(12): 1387-1398. doi: 10.3879/j.issn.1000-0887.2009.12.001

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Second-Order Sensitivity of Eigenpairs of Multiple Parameter Structures

doi: 10.3879/j.issn.1000-0887.2009.12.001

1.
College of Mechanical Science and Engineering, Nanling Campus, Jilin University, Changchun 130025, P. R. China;

Received Date: 2009-02-17
Rev Recd Date: 2009-10-15
Publish Date: 2009-12-15

Abstract

Abstract

A method for computing the second-order sensitivity matrix of eigenvalues and eigenvectors of the multiple parameter structures,i.e.the Hessian matrix,was presented.The second-order perturbations of eigenvalues and eigenvectors were transformed into the multiple parameter forms, and the second-order perturbation sensitivity matrices of eigenvalues and eigenvectors were developed.Using these formulations,the efficient methods based on the second-order Taylor expansion and second-order perturbation were obtained to estimate the changes of eigenvalues and eigenvectors when design parameters changed.The method avoided direct differential operation thus reducing the difficulty for computing the second-order sensitivity matrices of eigenpairs.A numerical example was given to demonstrate the application and the accuracy of the proposed methods.
- multiple parameter structures,
- second-order sensitivity of eigenpairs,
- efficient computational method

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References(22)

References

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