Sensitivity analysis of generalised eigenproblems and application to wave and finite element models

Sensitivity analysis of generalised eigenproblems and application to wave and finite element models

Cicirello, A. (TU Delft Mechanics and Physics of Structures; University of Oxford)
Mace, Brian (The University of Auckland)
Kingan, Michael (The University of Auckland)
Yang, Yi (The University of Auckland)

2020

The first and second order sensitivity analysis of the eigenvalue problem of generalised, nonsymmetric 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.

Generalised eigenproblems
Perturbation theory
Sensitivity analysis
Wave propagation
WFE

http://resolver.tudelft.nl/uuid:e37bb565-b331-48e5-a935-e1d82ece3931

https://doi.org/10.1016/j.jsv.2020.115345

0022-460X

Journal of Sound and Vibration, 478

Institutional Repository

journal article

© 2020 A. Cicirello, Brian Mace, Michael Kingan, Yi Yang