Sensitivity analysis of generalised eigenproblems and application to wave and finite element models. (21st July 2020)

• Record Type: Journal Article
• Authors: Cicirello, Alice; Mace, Brian R.; Kingan, Michael J.; Yang, Yi
• Is Part Of: Journal of sound and vibration. Volume 478(2020)
• Publication Date: 2020-07-21
• Subjects: Generalised eigenproblems -- Perturbation theory -- Wave propagation -- WFE -- Sensitivity analysis; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2020.115345
• Languages: English
• ISSNs: 0022-460X

Abstract

Abstract: The first and second order sensitivity analysis of the eigenvalue problem of generalised, non-symmetric matrices using perturbation theory is developed. These results are then applied to sensitivity analysis of wave propagation in structures modelled using the wave and finite element (WFE) method. Three formulations of the WFE eigenvalue problem are considered: the transfer matrix method, the projection method and Zhong's method. The sensitivities with respect to system parameters of wavenumbers and wave mode shapes are derived. Expressions for the group velocity are presented. Numerical results for a thin beam, a foam core panel and a cross-laminated timber panel are used to demonstrate the proposed approach. It is shown that sensitivities can be calculated at negligible computational cost.