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
 Citation: 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.

# Second-Order Sensitivity of Eigenpairs of Multiple Parameter Structures

##### doi: 10.3879/j.issn.1000-0887.2009.12.001
• Rev Recd Date: 2009-10-15
• Publish Date: 2009-12-15
• 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.
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