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

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

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.

• Jezik: Angleški jezik
• Ključne besede: guided waves, plates, soil dynamics, leaky waves, semi-analytical method, Zhang neural networks
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.04.2026
• Leto izida: 2026
• Št. strani: 17 str.
• Številčenje: Vol. 452, part B, art. no. 118763
• PID: 20.500.12556/RUL-178334
• UDK: 519.6
• ISSN pri članku: 0045-7825
• DOI: 10.1016/j.cma.2026.118763
• COBISS.SI-ID: 265875715
• Datum objave v RUL: 23.01.2026

Gradivo je del revije

• Naslov: Computer methods in applied mechanics and engineering
• Skrajšan naslov: Comput. methods appl. mech. eng.
• Založnik: Elsevier
• ISSN: 0045-7825
• COBISS.SI-ID: 6695685

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: vodeni valovi, plošče, dinamika tal, puščajoči valovi, semianalitične metode, Zhangove nevronske mreže

Projekti

• Financer: ARIS - Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
• Številka projekta: P1-0294
• Naslov: Računsko intenzivne metode v teoretičnem računalništvu, diskretni matematiki, kombinatorični optimizaciji ter numerični analizi in algebri z uporabo v naravoslovju in družboslovju

• Financer: French Government
• Program financ.: Investissements d’Avenir
• Številka projekta: ANR-10-LABX-24