Computation of leaky waves in layered structures coupled to unbounded media by exploiting multiparameter eigenvalue problems

Gravenkamp, Hauke (author), Plestenjak, Bor (author), Kiefer, Daniel A. (author), Jarlebring, Elias (author)

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.

• Language: English
• Keywords: guided waves, plates, soil dynamics, half-space, leaky waves, semi-analytical method
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.02.2025
• Year: 2025
• Number of pages: 22 str.
• Numbering: Vol. 596, [article no.] 118716
• PID: 20.500.12556/RUL-163828
• UDC: 519.6
• ISSN on article: 0022-460X
• DOI: 10.1016/j.jsv.2024.118716
• COBISS.SI-ID: 211164675
• Publication date in RUL: 11.10.2024

Record is a part of a journal

• Title: Journal of sound and vibration
• Shortened title: J. Sound Vib.
• Publisher: Elsevier
• ISSN: 0022-460X
• COBISS.SI-ID: 540946

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: vodeni valovi, plošče, dinamika tal, polprostor, puščajoči valovi, polanalitična metoda