TY - JOUR
T1 - Sensitivity analysis of generalised eigenproblems and application to wave and finite element models
AU - Cicirello, Alice
AU - Mace, Brian
AU - Kingan, Michael
AU - Yang, Yi
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Generalised eigenproblems
KW - Perturbation theory
KW - Sensitivity analysis
KW - Wave propagation
KW - WFE
UR - http://www.scopus.com/inward/record.url?scp=85083306324&partnerID=8YFLogxK
U2 - 10.1016/j.jsv.2020.115345
DO - 10.1016/j.jsv.2020.115345
M3 - Article
SN - 0022-460X
VL - 478
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
M1 - 115345
ER -