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.

Dispersion curves of elastic waveguides exhibit points where the group velocity vanishes while the wavenumber remains finite. These are the so-called zero-group-velocity (ZGV) points. As the elastodynamic energy at these points remains confined close to the source, they are of practical interest for nondestructive testing and quantitative characterization of structures. These applications rely on the correct prediction of the ZGV points. In this contribution, we first model the ZGV resonances in anisotropic plates based on the appearance of an additional modal solution. The resulting governing equation is interpreted as a two-parameter eigenvalue problem. Subsequently, we present three complementary numerical procedures capable of computing ZGV points in arbitrary nondissipative elastic waveguides in the conventional sense that their axial power flux vanishes. The first method is globally convergent and guarantees to find all ZGV points but can only be used for small problems. The second procedure is a very fast, generally-applicable, Newton-type iteration that is locally convergent and requires initial guesses. The third method combines both kinds of approaches and yields a procedure that is applicable to large problems, does not require initial guesses and is likely to find all ZGV points. The algorithms are implemented in GEW ZGV computation (doi: 10.5281/zenodo.7537442).

Layer thickness and the speed of sound are important parameters for nondestructive testing applications. If one of the parameters is known, the other one can be determined by simple time-of-flight (TOF) measurement of ultrasound. However, often these parameters are both unknown. In this contribution, we examine and adapt ultrasonic imaging techniques using coded excitation signals to simultaneously measure the thickness and the speed of sound of homogeneous elastic plates of unknown material. Good axial resolution is required to measure thin samples. We present a new approach for transmission signal conditioning to improve axial resolution. This conditioning consists of enhancing spectral components that are damped by the transducer prior to transmit. Due to the long duration of coded excitation signals, pulse compression techniques are required for TOF measurements. Common pulse compression filters are discussed, and appropriate filtering of the compression waveform is designed to keep the sidelobe level (SLL) acceptably low. An experimental assessment of the presented measurement techniques reveals that the signal conditioning substantially increases the axial resolution. However, a tapered Wiener filter should be used for the best tradeoff between SLL and axial resolution. We used the proposed method to measure different plates of steel, aluminum, and polymethylmethacrylate of various thicknesses, and the results show very good agreement with the reference values, which we obtained with a micrometer screw and by standard TOF measurement, respectively. The relative error for the plate thickness is smaller than 2.2% and that for the speed of sound is smaller than 3%. It is remarkable that plate thickness could be measured down to 60% of the wavelength.

Elastic waves in anisotropic media can exhibit a power flux that is not collinear with the wave vector. This has notable consequences for waves guided in a plate. Through laser-ultrasonic experiments, we evidence remarkable phenomena due to slow waves in a single-crystal silicon wafer. Waves exhibiting power flux orthogonal to their wave vector are identified. A pulsed line source that excites these waves reveals a wave packet radiated parallel to the line. Furthermore, there exist precisely eight plane waves with zero power flux. These so-called zero–group-velocity modes are oriented along the crystal’s principal axes. Time acts as a filter in the wave-vector domain that selects these modes. Thus, a point source leads to beating resonance patterns with moving nodal curves on the surface of the infinite plate. We observe this pattern as it emerges naturally after a pulsed excitation.