Computation of leaky waves in layered structures coupled to unbounded media by exploiting multiparameter eigenvalue problems
Abstract
We present a semi-analytical approach to compute quasi-guided elastic wave modes in horizontally layered structures radiating into unbounded fluid or solid media. This problem is of relevance, e.g., for the simulation of guided ultrasound in embedded plate structures or seismic waves in soil layers over an elastic half-space. We employ a semi-analytical formulation to describe the layers, thus discretizing the thickness direction by means of finite elements . For a free layer, this technique leads to a well-known quadratic eigenvalue problem for the mode shapes and corresponding horizontal wavenumbers. Incorporating the coupling conditions to account for the adjacent half-spaces gives rise to additional terms that are nonlinear in the wavenumber. We show that the resulting nonlinear eigenvalue problem can be cast in the form of a multiparameter eigenvalue problem whose solutions represent the wave numbers in the plate and in the half-spaces. The multiparameter eigenvalue problem is solved numerically using recently developed algorithms. Matlab implementations of the proposed methods are publicly available.
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BibTeX
@article{gravenkamp2026computation,
title = {{Computation of leaky waves in layered structures coupled to unbounded media by exploiting multiparameter eigenvalue problems}},
author = {Hauke Gravenkamp and Bor Plestenjak and Daniel Kiefer and Elias Jarlebring},
journal = {Journal of Sound and Vibration},
year = {2026},
month = oct,
doi = {10.1016/j.jsv.2024.118716},
eprint = {2404.15277},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05786309v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Computation of leaky waves in layered structures coupled to unbounded media by exploiting multiparameter eigenvalue problems
AU - Hauke Gravenkamp
AU - Bor Plestenjak
AU - Daniel Kiefer
AU - Elias Jarlebring
PY - 2026
DA - 2026/10/08
JO - Journal of Sound and Vibration
DO - 10.1016/j.jsv.2024.118716
UR - https://hal.science/hal-05786309v1
AB - We present a semi-analytical approach to compute quasi-guided elastic wave modes in horizontally layered structures radiating into unbounded fluid or solid media. This problem is of relevance, e.g., for the simulation of guided ultrasound in embedded plate structures or seismic waves in soil layers over an elastic half-space. We employ a semi-analytical formulation to describe the layers, thus discretizing the thickness direction by means of finite elements . For a free layer, this technique leads to a well-known quadratic eigenvalue problem for the mode shapes and corresponding horizontal wavenumbers. Incorporating the coupling conditions to account for the adjacent half-spaces gives rise to additional terms that are nonlinear in the wavenumber. We show that the resulting nonlinear eigenvalue problem can be cast in the form of a multiparameter eigenvalue problem whose solutions represent the wave numbers in the plate and in the half-spaces. The multiparameter eigenvalue problem is solved numerically using recently developed algorithms. Matlab implementations of the proposed methods are publicly available.
SN - 0022-460X
SN - 1095-8568
ER -