Willy Thys

Experimental and theoretical study of Lamb wave dispersion in aluminum/polymer bilayers

This paper deals with the dispersion of Lamb waves in solid bilayers obtained by coating a 0.61‐mm‐thick aluminum plate with a polymer of thickness between 180 and 500 μm. The theoretical dispersion curves of the bilayers in air are analyzed in terms of the dispersion in the decoupled layers, the aluminum substratum, and the polymer coating, respectively. Because of the smaller acoustic impedance of the polymer coating, it behaves in the bilayer as if it were rigidly held by the aluminum substratum. The side of the polymer facing air is considered to be stress‐free. The decoupled aluminum plate is modeled as if it were stress‐free on both sides. The approximate boundary conditions for the coating are verified by a separate experiment. The experimental data obtained by means of a double transmission immersion technique, confirm the numerical analysis. Not all theoretically predicted modes are observed. The results show how coupling between the Lamb modes of the aluminum substratum, and those of the polymer coating, makes the bilayer switch between modes. Displacement and stress profiles are used to further elucidate the analysis. In the last paragraph a simple mechanical model composed of two masses and three springs, is analyzed. It exhibits mode coupling and mode switching in a way which is very similar to that found for these solid bilayers.

Mode coupling in solid/liquid/solid trilayers

This paper deals with elastic wave dispersion in trilayers composed of two solid plates (glass or aluminum) separated by a thin water layer. Two symmetrical (identical top and bottom layers) and two asymmetrical trilayers are investigated. It is shown that the dispersion curves of a trilayer can be analyzed in terms of the dispersion in the decoupled constituent layers, provided that the appropriate boundary conditions are used and that mode coupling between the modes of the decoupled layers is taken into account. The experimental data obtained by means of a double transmission immersion technique confirm this analysis. The main conclusions reached are (i) that the normal propagation modes of the decoupled constituents determine the asymptotic behavior of the trilayer modes; and (ii) that successive mode coupling is responsible for the course of the trilayer modes. Further, numerical and experimental evidence is found that doublets are formed around the modes of the decoupled solid plates in symmetrical b...

Experimental observation on a frequency spectrum of a plate mode of a predominantly leaky nature

The problem of normal propagation modes of a plate submerged in a fluid is usually treated by considering continuous leaky Lamb waves or by considering transient waves. Angular plate resonances are associated with modes obtained by the first approach, whereas frequency plate resonances are associated with modes obtained using the second method. The dispersion curves for these two kinds of mode are almost identical, except for certain modes at large phase speed. In an experiment one is never dealing with one of these extreme situations because the applied signal is never infinitely long and the beam used to insonify the plate is never infinitely wide. In this paper we report on the manifestation in the transmission frequency spectrum, of a plate mode of a predominantly leaky nature. The extra mode, which has never been reported on, is observed between the cutoff frequencies of the symmetrical transient modes S1 and S2 of a submerged aluminium plate. The modes are identified by means of an Argand diagram.

Experimental and theoretical study of elastic wave dispersion in a liquid bilayer

A model is constructed to express the normal dispersion curves of a liquid bilayer in terms of the dispersion curves of its two constituent layers. The idea is illustrated with a numerical example and later experimentally confirmed with another example.

Experimental data supporting calculations of the angular derivative of the phase of the transmission coefficient of an elastic plate

Abstract From theory it is predicted that Lamb modes having a positive group velocity and those having a negative group velocity correspond to, respectively, negative and positive peaks on a spectrum showing the angular derivative of the phase of the transmission coefficient of the elastic plate. Experimental data are presented here that support this prediction.

The angular resolution of Lamb mode detection

It is shown experimentally that the angular resolution of Lamb mode detection can be strongly enhanced by properly positioning the detector in the ‘‘leaky’’ field. For this purpose we studied a 1‐mm‐thick aluminum plate (140 mm×200 mm) which has two pairs of closely spaced Lamb modes (s1,a1 and s0,a0) in the frequency region between 3 and 4 MHz. In order to obtain the necessary spatial resolution, the Lamb spectrum is measured by means of an acousto‐optical technique with a small aperture photodiode as detector. It turns out that for each pair of closely spaced modes, there is a detector position in the leaky field where the angular resolution is optimal. These results are explained by analyzing the acoustic profiles transmitted by the plate at different angles of incidence.

The frequency width of symmetric modes of an aluminum plate: manifestation of a complex slowness on a frequency spectrum

The evolution of the experimental frequency width of symmetric modes of an aluminum plate is studied as a function of the angle of incidence below the first critical angle. It is found that the frequency width predicted by resonant scattering theory, corrected for the directivity of emitter and receiver, generally explains the experimental frequency width well. However, large discrepancies remain for the frequency width of the S1 mode at angles of incidence larger than 9 degrees. It is demonstrated that these are caused by not taking into account the complex nature of the slowness of the plate mode. This suggests that there is a need for a theory that models the interaction of a beam of ultrasound, bounded in space and time, with an elastic plate.

Experimental determination of the angular width of plate modes

The reflection and transmission coefficient of a plate can be expressed as a function of frequency at fixed angle of incidence or as a function of angle of incidence at fixed frequency. In the first situation, the transmission coefficient can be considered as a superposition of frequency resonances, while in the latter case it can be considered as a superposition of angular resonances [R. Fiorito, W. Madigosky, and H. Uberall, J. Acoust. Soc. Am. 66, 1857–1866 (1979)]. Using this approximation the properties of frequency resonances of a plate can be determined experimentally [Derible et al., Ultrasonics International 93 Conf. Proc. 483–486 (1993)]. In this work, this approximation is used to determine the properties of the angular resonances. The transmission coefficient as a function of frequency is determined for a large set of angles of incidence by insonifying the plate with an ultrasonic pulse. Then, at fixed frequency, the data are plotted as a function of angle of incidence. The properties of the a...

High‐resolution spectroscopy of the Lamb modes of a plate near normal incidence

Using a high‐resolution digital oscilloscope and advanced datahandling plate modes near normal incidence, other than those identified by Lamb, were studied. This search was led by the complex roots of the dispersion relation for a plate in water. Solutions with a complex wave number component in the propagation direction indeed reveal near normal incidence the existence of plate modes no one has ever observed to our knowledge. In this paper experimental results are presented at the cutoff frequencies of the S1 and S2 modes of a 1.5‐mm‐thick aluminum plate, and at the cutoff frequencies of the A1 and A2 modes of a 1.5‐mm‐thick glass plate. The extra resonance predicted by the theory is resolved by looking at the time history of the radiating plate. This is done either by displacing the time window far into the free emission regime or by displacing the receiving transducer in the propagation direction.

Mode coupling in Al/polymer bilayers

This paper deals with the dispersion of Lamb waves in solid bilayers. The theoretical dispersion curves of the bilayers in air are analyzed in terms of the dispersion in the decoupled layers. Experimental data confirm the numerical analysis. The results show how coupling between the Lamb modes of the substrate and those of the coating makes the bilayer switch between modes.