Jean-Louis Izbicki

Resonances of plates and cylinders: Guided waves

The study of the normal diffusion of an ultrasonic plane wave by cylinders and plates imbedded in the water shows resonances which are the natural modes of vibration. When a natural mode of an elastic target is excited, the energy which is stored during the forced excitation is emitted after the end of the forced excitation. The observation of backscattered spectra obtained by the Resonance Isolation and Identification Method (RIIM) from an aluminum cylinder shows supplementary resonances. The directivity pattern of the transducer is the cause of these supplementary resonances. The behavior of these resonances is analogous to the resonances of the plate. This leads us to study the natural modes of the cylinder. All the resonances which are experimentally detected may be considered as normal modes of the target. The results obtained on plates and cylinders have a common point: the generation of a guided wave by the excitation of a resonance.

Ultrasonic guided waves on a periodical grating: Coupled modes in the first Brillouin zone

The propagation of Lamb waves in a plate with an engraved periodic grating is addressed in this article. Mode conversions and reflections are analyzed. In the first part the conversion modes are explained by the existence of a resonance condition between the Lamb-wave wavenumbers and the fundamental and harmonic spatial periods of the grating. These phenomena are experimentally and numerically highlighted for a metallic waveguide with a rectangular grating. The second part focuses on the pseudo-Lamb wave dispersion curves in a periodic waveguide. The periodicity implies that the Lamb waves dispersion curves fold back at the edge of the Brillouin zone. Several stop bands appear: classical band gaps at the boundary of the Brillouin zone and mini-stop-bands inside the Brillouin zone. For the ministop band, dispersion curves cross and a possible coupling occurs between the modes. Finally, conversions or the existence of gaps are linked with the Power Spectral Density of the grating profile.

Relation between surface helical waves and elastic cylinder resonances

In this paper, the authors deal with theoretical and experimental studies about the acoustic scattering by an elastic solid cylinder immersed in water, at oblique incidence. Comparisons are made between the calculated form function and measured scattered pressure for incidence angles varying from 0° to 30°, in the normalized frequency range 0–30. The behavior of the resonances when the incidence angle increases is shown and the connection between helical surface waves propagation and resonance is explained, using the contributions of the resonance scattering theory and the Sommerfeld–Watson transformation. More accurately, resonances are due to the phase matching of circumnavigating helical surface waves, and a refraction effect is found to take place between the incident and the helical surface wave direction of propagation, which clearly explains the resonance shift with respect to incidence angle variations. Guided waves appear at oblique incidence with a polarization primarily transverse at small inci...

Propagation of Lamb waves in a plate with a periodic grating: Interpretation by phonon

In this paper the propagation of Lamb waves in an aluminium plate with a periodic grating containing triangular grooves is studied. Numerical simulations (FEM) are performed. A single incident mode is excited on a flat area and the interaction with the periodic grating is studied. Reflected converted waves are observed when the incident Lamb wave passes through the grating. At the entrance of the periodic grating, a phonon relation is written between the incident signal, the converted mode, and the phonon related to the grating. An experimental verification of the phonon relation is carried out.

Influence of the free modes of vibration on the acoustic scattering of a circular cylindrical shell

The scattering of an acoustic wave by an elastic circular cylindrical shell immersed in water depends on the natural modes of the target. Two groups of natural modes may be considered. The first group is related to circumferential waves which propagate around the tube. These resonances are provided by the resonance scattering theory. The second group is related to waves whose direction of propagation is parallel to the axis of the tube. The calculation of the natural modes and the experimental data obtained by the ‘‘method of isolation and identification of the resonances’’ agree very well.

Study of Lamb waves based upon the frequency and angular derivatives of the phase of the reflection coefficient

This article deals with the introduction of a new method which allows the complete characterization of an elastic plate, on the one hand, in terms of resonances and, on the other hand, in terms of Lamb wave propagation. It is based upon the study of the derivatives of the reflection coefficient phase, considered either as a function of a frequency variable or as a function of an angular variable. When the Breit–Wigner approximation is valid, i.e., when the poles of the reflection coefficient are close to the real axis, the comparison with the resonant scattering theory (RST) leads to the characterization of frequency or angular resonances in terms of positions and widths, by means of the location and of the magnitude of the phase derivative peaks. Moreover, this method allows one to establish the important link between this resonant theory derived from the RST and the normal mode theory of propagation. So, the width of a resonance is explicitly related to the imaginary part of the wave vector of the assoc...

Bending A wave in the scattering by a circular cylindrical shell: Its relation with the bending free modes

The steady‐state problem of a plane acoustic wave scattered by an elastic circular cylindrical shell is considered. The standard resonance scattering theory (RST) procedure is used for the analysis of modal resonances. The bending waves, namely A and A0 waves, are investigated in detail. At a fixed order of modal resonance n, it is possible to obtain either the A wave resonance, or the A0 wave resonance, but never both of them together. The relation between the modal resonances of the peripheral waves A and A0 and the free modes of vibration of the shell is studied by means of the variation of the density ρ of the ambient liquid. When the density of the ambient liquid tends toward zero (at unchanged sound velocity in it), the resonance frequency approaches the one of the free vibration in two different ways. If the wave associated with the free mode has a velocity greater than the sound velocity in the fluid, the A0 wave resonance frequency tends to that of the free mode. If the wave associated with the f...

Lamb wave attenuation in a rough plate. I. Analytical and experimental results in an anisotropic plate

The characterization of bounded roughened surfaces before applying adhesive joint, in order to detect poor cohesive and adhesive properties, remains difficult. Earlier studies based on analysis of surface wave (Rayleigh waves or Scholte waves) are not really adapted to the characterization of such surfaces. Guided acoustic waves, i.e., Lamb waves, turn out to be the best adapted kind of waves to characterize this roughness when plates are bounded together. It is the aim of this paper to provide analytical and experimental approaches to analyze the behavior of Lamb waves propagating inside plates with a rough surface (small perturbations). First, experimental results of the attenuation effects are given on roughened glass plates. Second, the attenuation factor of the Lamb wave in an anisotropic rough solid plate is calculated through a complex analytical model of the dispersion equation which accounts for the effect of the power spectrum density of the rough profile (including the effect of the statistical...

Acoustic scattering from cylindrical shells: Guided waves and resonances of the liquid column

Abstract Recent studies of acoustic scattering have allowed the explanation of the existence of additional lines in the resonance spectrum of an elastic solid cylinder immersed in water by the examination of natural modes. A first group of natural modes, related to the propagation of the circumferential waves (Rayleigh, Whispering Gallery waves), is detected when the cylinder is insonified perpendicularly to its axis. A second group of natural modes related to the guided waves which propagate in the direction parallel to the axis of the cylinder is detected when it is insonified obliquely. In this Paper, the authors examine the acoustic scattering from cylindrical shells filled with a fluid (air or liquid) by the method of isolation and identification of resonances (MIIR). It allows resonance spectra to be obtained; in addition, the mode number, n , given by the identification, makes it possible to separate the resonances into different series. It is possible to explain the experimental resonance spectra of a liquid-filled tube insonified perpendicularly to its axis with a non-perfect directive transducer, by the calculation of the eigenfrequencies of the different parts of the target. The authors show the great importance of the guided waves along the axis and of the resonances of the liquid column when the shell is filled with a liquid. The resonance spectra of liquid-filled targets and the reradiation patterns giving by MIIR, i.e. after the end of excitation, are shown for the first time.

Methode impulsionnelle numerisee (MIN) pour l'isolement et l'identification des resonances de tubes immerges

Abstract The method of isolation and identification of resonances (MIIR) allows a direct verification of “resonance scattering theory” (RST). Indeed it provides the resonance spectra of aluminum elastic cylindrical shells, insonified by plane acoustic waves and it also allows the experimental determination of the mode number of each resonance of the target. At this day, when the shells are insonified by a short pulse it is only possible to obtain the resonance spectrum with a fast Fourier transform of the backscattered response. This paper presents an impulse method which allows the isolation of resonances and besides the identification of each eigenmode of the target.