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°. 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.

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 transmission frequency spectrum at normal incidence of a water-loaded glass plate has been studied searching for modes of a predominantly leaky nature. Near the cut-off frequency of the mode A2, an antisymmetric mode A3'of a predominantly leaky nature was observed in the frequency spectrum of the leaky field. The mode A3' is completely separated from the neighbouring modes A2 and A3 by displacing the time-window of the recording oscilloscope into the free-emission regime. It is demonstrated that plate modes of a different nature contribute to the specular acoustic field and to the leaky field.

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 angular resonances are extracted using the Argand representation of the transmission coefficient. A comparison with theoretical values is made.

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.

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.

A method to determine the transversal wave velocity in submerged plates is presented. It is based on an analysis of the transmission coefficient of the plate between its first and second critical angles, where the only bulk waves present in the plate are shear waves. According to the resonance theory of plate modes, the parametric representation of the transmission coefficient of a plate in the complex plane (an Argand diagram) is a circle. It turns out that the experimental Argand diagram can be given the same orientation as the theoretical diagram by introducing a time-delay between the transmitted and the reference signal during the normalisation process. Between the first and second critical angles, this time-delay depends on the transversal wave velocity only. We propose to determine the time-delay required for a correct orientation of the Argand diagram and to calculate from it the transversal wave velocity.

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 but not in asymmetrical trilayers. It will be shown that mode coupling between two identical modes of the top and bottom layer is responsible for these doublets. Plots of the modulus and the phase of the reflection coefficient of the trilayers, as a function of frequency, further elucidate the analysis.

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.

This paper investigates numerically and experimentally how a standing wave is built up in an air column by a sound burst. Special attention is paid to the transient regimes at the front end and the beck end of the burst. The standing wave is modelled mathematically as the superposition of plane waves multiply reflected on the ends of the air column. Several special cases are discussed. The frequency of the burst is either on or off resonance. The length of the burst is either long or short compared with the time the sound needs to travel up and down the air column. The experimental results obtained with a tube and a loudspeaker are in agreement with the numerical results apart from the distortion caused by the loudspeaker. It is also shown how the transfer function of the air column can be obtained from the response to a sound burst. The transfer function is decomposed in a Breit-Wigner resonance form.

In this paper we analyse the dispersion of the normal propagation modes of a liquid bilayer in terms of the dispersion in the constituent layers with the proper boundary conditions. The analysis is done in the framework of an acoustic raymodel which leads to a transparent form of the dispersion relation. Although a liquid bilayer is of no direct practical use, the data analysis will prove to be of great help when studying solid multilayers.