Calculating the full leaky Lamb wave spectrum with exact fluid interaction

Journal article

Publication Details

Author(s): Kiefer DA, Ponschab M, Rupitsch S, Mayle M
Journal: Journal of the Acoustical Society of America
Publication year: 2019
Volume: 145
Journal issue: 6
Pages range: 3341--3350
ISSN: 0001-4966


Lamb waves are elastodynamic guided waves in plates and are used for non-destructive evaluation, sensors, and material characterization. These applications rely on the knowledge of the dispersion characteristics, i.e., the frequency-dependent wavenumbers. The interaction of a plate with an adjacent fluid leads to a nonlinear differential eigenvalue problem with a square root term describing exchange of energy with the surrounding medium, e.g., via acoustic radiation. In this contribution, a spectral collocation scheme is applied to discretize the differential eigenvalue problem. A change of variable is performed to obtain an equivalent polynomial eigenvalue problem of fourth order, which is linear in state-space and can reliably be solved using modern numerical methods. Traditionally, the leaky Lamb wave problem has been solved by finding the roots of the characteristic equations, a numerically ill-conditioned problem. In contrast to root-finding, the approach described in this paper is inherently able to find all modes and naturally handles complex wavenumbers. The full phase velocity dispersion diagram and attenuation curves are presented and are shown to be in excellent agreement with solutions of the characteristic equation as well as computations made with a perturbation method. The procedure is applicable to anisotropic, viscoelastic, inhomogeneous, and layered plates coupled to an inviscid fluid.

FAU Authors / FAU Editors

Kiefer, Daniel A.
Lehrstuhl für Sensorik
Ponschab, Michael
Lehrstuhl für Sensorik
Rupitsch, Stefan PD Dr.
Lehrstuhl für Sensorik

How to cite

Kiefer, D.A., Ponschab, M., Rupitsch, S., & Mayle, M. (2019). Calculating the full leaky Lamb wave spectrum with exact fluid interaction. Journal of the Acoustical Society of America, 145(6), 3341--3350.

Kiefer, Daniel A., et al. "Calculating the full leaky Lamb wave spectrum with exact fluid interaction." Journal of the Acoustical Society of America 145.6 (2019): 3341--3350.


Last updated on 2019-18-06 at 16:23