Continuation Approach Combined with Semi-Analytical Finite-Element Method for Solving Guided-Wave Dispersion Equation

The present article introduces a tracing algorithm for dispersion curves for guided waves. The quadratic eigenvalue problem for dispersion analysis is constructed in a semi-analytical finite-element model. The eigenvalue problem is converted into a system of nonlinear equations by introducing phase...

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Veröffentlicht in:Journal of nondestructive evaluation Jg. 44; H. 2; S. 55
Hauptverfasser: Maruyama, Taizo, Nakahata, Kazuyuki
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.06.2025
Springer Nature B.V
Schlagworte:
Algorithms
Characterization and Evaluation of Materials
Classical Mechanics
Continuation methods
Control
Decomposition
Dispersion curve analysis
Dynamical Systems
Eigenvalues
Eigenvectors
Engineering
Finite element method
Mathematical analysis
Nondestructive testing
Nonlinear equations
Open source software
Solid Mechanics
Tracing
Vibration
Viscosity
Wave dispersion
Guided wave
Curve tracing
Mode veering
Numerical continuation method
Dispersion curve
Semi-analytical finite-element method
ISSN:0195-9298, 1573-4862
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Zusammenfassung:The present article introduces a tracing algorithm for dispersion curves for guided waves. The quadratic eigenvalue problem for dispersion analysis is constructed in a semi-analytical finite-element model. The eigenvalue problem is converted into a system of nonlinear equations by introducing phase and amplitude conditions for the eigenvector. Solutions of the system of nonlinear equations are traced by means of a numerical continuation method (NCM). The proximity of dispersion curves, which is referred to as mode veering, becomes a problem in the NCM tracing process. In order to overcome the mode-veering issue, constraints on the tangential and curvature vectors for the dispersion curve are proposed. Several numerical results demonstrate that the proposed NCM can trace dispersion curves appropriately, even for mode-veering cases. Furthermore, the group velocities of guided waves can be calculated easily and accurately in the proposed formulation.
Bibliographie:ObjectType-Article-1
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ISSN:0195-9298
1573-4862
DOI:10.1007/s10921-025-01194-w