Computing leaky waves in semi-analytical waveguide models by exponential residual relaxation

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

Semi-analytical methods for modeling guided waves in structures of constant cross-section yield frequency-dependent polynomial eigenvalue problems for the wavenumbers and mode shapes. Solving these eigenvalue problems over a range of frequencies results in continuous eigencurves. Recent research has shown that eigencurves of differentiable parameter-dependent eigenvalue problems can alternatively be computed as solutions to a system of ordinary differential equations (ODEs) obtained by postulating an exponentially decaying residual of a modal solution. Starting from an approximate initial guess of the eigenvalue and eigenvector at a given frequency, the complete eigencurve is obtained using standard numerical ODE solvers. We exploit this idea to develop an efficient method for computing the dispersion curves of plate structures coupled to unbounded solid or fluid media. In these scenarios, the approach is particularly useful because the boundary conditions give rise to nonlinear terms that severely hinder the application of traditional solvers. We discuss suitable approximations of the nonlinearity for obtaining initial values, analyze computational costs and robustness of the proposed algorithm, and verify results by comparison against existing methods.

• Language: English
• Keywords: guided waves, plates, soil dynamics, leaky waves, semi-analytical method, Zhang neural networks
• 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: 01.04.2026
• Year: 2026
• Number of pages: 17 str.
• Numbering: Vol. 452, part B, art. no. 118763
• PID: 20.500.12556/RUL-178334
• UDC: 519.6
• ISSN on article: 0045-7825
• DOI: 10.1016/j.cma.2026.118763
• COBISS.SI-ID: 265875715
• Publication date in RUL: 23.01.2026

Record is a part of a journal

• Title: Computer methods in applied mechanics and engineering
• Shortened title: Comput. methods appl. mech. eng.
• Publisher: Elsevier
• ISSN: 0045-7825
• COBISS.SI-ID: 6695685

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, puščajoči valovi, semianalitične metode, Zhangove nevronske mreže

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0294
• Name: Računsko intenzivne metode v teoretičnem računalništvu, diskretni matematiki, kombinatorični optimizaciji ter numerični analizi in algebri z uporabo v naravoslovju in družboslovju

• Funder: French Government
• Funding programme: Investissements d’Avenir
• Project number: ANR-10-LABX-24