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Computation of leaky waves in layered structures coupled to unbounded media by exploiting multiparameter eigenvalue problems
Int Ctr Numer Methods Engn CIMNE, Barcelona 08034, Spain..
IMFM, Jadranska 19, SI-1000 Ljubljana, Slovenia.;Univ Ljubljana, Fac Math & Phys, Jadranska 19, Ljubljana SI-1000, Slovenia..
Univ PSL, Inst Langevin, ESPCI Paris, CNRS, F-75005 Paris, France..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, Optimization and Systems Theory.ORCID iD: 0000-0001-9443-8772
2025 (English)In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 596, article id 118716Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Academic Press, 2025. Vol. 596, article id 118716
Keywords [en]
Guided waves, Plates, Soil dynamics, Half-space, Leaky waves, Semi-analytical method
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-355319DOI: 10.1016/j.jsv.2024.118716ISI: 001334187600001Scopus ID: 2-s2.0-85205908869OAI: oai:DiVA.org:kth-355319DiVA, id: diva2:1908901
Note

QC 20241029

Available from: 2024-10-29 Created: 2024-10-29 Last updated: 2024-10-29Bibliographically approved

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Jarlebring, Elias

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