Laser beam shaping for enhanced Zero-Group Velocity Lamb modes generation

Optimization of Lamb modes induced by laser can be achieved by adjusting the spatial source distribution to the mode wavelength ($\lambda$). The excitability of Zero-Group Velocity (ZGV) resonances in isotropic plates is investigated both theoretically and experimentally for axially symmetric sources. Optimal parameters and amplitude gains are derived analytically for spot and annular sources of either Gaussian or rectangular energy profiles. For a Gaussian spot source, the optimal radius is found to be $\lambda_{ZGV}/\pi$. Annular sources increase the amplitude by at least a factor of 3 compared to the optimal Gaussian source. Rectangular energy profiles provide higher gain than Gaussian ones. These predictions are confirmed by semi-analytical simulation of the thermoelastic generation of Lamb waves, including the effect of material attenuation. Experimentally, Gaussian ring sources of controlled width and radius are produced with an axicon-lens system. Measured optimal geometric parameters obtained for Gaussian and annular beams are in good agreement with theoretical predictions. A ZGV resonance amplification factor of 2.1 is obtained with the Gaussian ring. Such source should facilitate the inspection of highly attenuating plates made of low ablation threshold materials like composites.Comment: 11 pages, 12 figure

Laser induced Zero-Group Velocity resonances in Transversely Isotropic cylinder

The transient response of an elastic cylinder to a laser impact is studied. When the laser source is a line perpendicular to the cylinder axis, modes guided along the cylinder are generated. For a millimetric steel cylinder up to ten narrow resonances can be locally detected by laser interferometry below 8 MHz. Most of these resonances correspond to Zero-Group Velocity guided modes while a few others can be ascribed to thickness modes. We observe that the theory describing the propagation of elastic waves in an isotropic cylinder is not sufficient to precisely predict the resonance spectrum. In fact, the texture of such elongated structure manifest as elastic anisotropy. Thus, a transverse isotropic (TI) model is used to calculate the dispersion curves and compare them with the measured one, obtained by moving the source along the cylinder. The five elastic constants of a TI cylinder are adjusted leading to a good agreement between measured and theoretical dispersion curves. Then, all the resonance frequencies are satisfactorily identified.Comment: 23 pages, 7 figures, submitted to the JAS

Negative reflection of elastic guided waves in chaotic and random scattering media

The propagation of waves in complex media can be harnessed either by taming the incident wave-field impinging on the medium or by forcing waves along desired paths through its careful design. These two alternative strategies have given rise to fascinating concepts such as time reversal or negative refraction. Here, we show how these two processes are intimately linked through the negative reflection phenomenon. A negative reflecting mirror converts a wave of positive phase velocity into its negative counterpart and vice versa. In this article, we experimentally demonstrate this phenomenon with elastic waves in a 2D billiard and in a disordered plate by means of laser interferometry. Despite the complexity of such configurations, the negatively reflected wave field focuses back towards the initial source location, thereby mimicking a phase conjugation operation while being a fully passive process. The super-focusing capability of negative reflection is also highlighted in a monochromatic regime. The negative reflection phenomenon is not restricted to guided elastic waves since it can occur in zero-gap systems such as photonic crystals, chiral metamaterials or graphene. Negative reflection can thus become a tool of choice for the control of waves in all fields of wave physics.Comment: 9 pages, 6 figure

Non-destructive testing of composite plates by holographic vibrometry

We report on a wide-field optical monitoring method for revealing local delaminations in sandwich-type composite plates at video-rate by holographic vibrometry. Non-contact measurements of low frequency flexural waves is performed with time-averaged heterodyne holography. It enables narrowband imaging of local out-of-plane nanometric vibration amplitudes under sinusoidal excitation, and reveals delamination defects, which cause local resonances of flexural waves. The size of the defect can be estimated from the first resonance frequency of the flexural wave and the mechanical parameters of the observed layer of the composite plate

Beating resonance patterns and orthogonal wave propagation due to zero-group-velocity guided elastic waves

Elastic waves in anisotropic media can exhibit a power flux that is not collinear with the wave vector. We show that this has remarkable consequences for the zero-group-velocity (ZGV) resonances that appear in an infinite plate. True ZGV resonances, in the sense that the guided wave's overall power flux vanishes while its wavelength remains finite, are only found when the wave vector is oriented along a principal axis of the material. At other propagation angles, "quasi-ZGV" waves are found for which the power flux is orthogonal to the wave vector. We present original measurements of such a wave field in a single crystal silicon wafer. As a consequence of the nonzero power flux of qZGV waves, time acts as a filter in the wave vector domain that selects precisely the eight plane waves corresponding to true ZGV resonances. This intuitively explains the highly symmetric resonance pattern that emerges naturally on the surface of the plate after a pulsed point source excitation. We showcase a direct measurement of this beating pattern. The developed physical understanding paves the way towards novel designs of surface acoustic wave devices and is of high relevance for ultrasonic nondestructive evaluation.Comment: 10 pages, 9 figure

Experimental Study of Probe-Sample Contact Influence on Dispersion Curve Measurement with Phased Arrays in Plates

Dispersion curves of guided modes in plate-like structure are used to investigate elastic properties. Laser based ultrasound are conventional contactless techniques to acquire dispersion curves. Measurements are broadband and quite sensitive but time consuming. Linear transducer arrays in contact with the sample can also be used to generate and measure guided modes in plate. Measurements are limited by the probe’s bandwidth to few MHz but are really fast. An array response matrix is used to improve the signal processing with a singular value decomposition (SVD) filtering and plane wave subspace projection [1]. A contact gel is used to allow the ultrasound transmission from the transducers to the sample, which may lead to some issues. Indeed, the contact modifies the stress boundary conditions on the sample. Simulations are performed to observe the dispersion curves variations induced by the contact. Modifications are showed to occur mainly around points where group velocity vanishes. Experiments are conducted in aluminum-epoxy-aluminum tri-layer structures. Some new features on SVD techniques are performed on phased array measurements to provide the dispersion curves. Comparison with laser based ultrasound measurements shows good agreement between the two techniques into the shared bandwidth. These results show that linear transducer array provides reliable and precise dispersion curves in a very fast manner