O. Lenoir

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...

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...

Acoustic scattering from an immersed plane multilayer : application to the inverse problem

The authors deal with acoustic scattering from a plane multilayered structure. This structure is composed of a first plastic elastic layer, a thin water layer, and a second aluminum elastic layer. A pulse excitation is used to obtain the scattered spectra and the resonance spectra at normal and oblique incidence. These spectra give information about the structure. The spectra of resonances due to the guided waves provide information about the resonant character of the two elastic solids. The farther the guided waves propagate in a layer, the more resonant the layer is. These guided waves are Lamb waves of the solid layers. The backscattered signal is formed by a series of echoes which arise from the different layers of the structure. With simple experiments, involving in particular a temporal filtering of the reflected signal, it is shown that it is possible to obtain three of the four parameters which characterize the solid layers: the phase velocities of the longitudinal waves, thicknesses, and densitie...

Acoustic radiation of cylindrical elastic shells subjected to a point source: Investigation in terms of helical acoustic rays

The paper deals with the acoustic radiation of a cylindrical elastic shell with no internal loading surrounded by a fluid medium when its external surface is subjected to a point source. The problem is addressed via the use of the spatial Fourier transform. An expression is obtained for the radiated pressure that is evaluated for the far field using both the stationary phase method and the fast Fourier transform (FFT). The acoustic field calculated from the FFT is much more complicated than that obtained by using only the stationary phase method. In agreement with the geometrical theory of diffraction (GTD), alternative interpretations of the radiated field in terms of helical acoustic rays allows one to understand the reason for this result. The outstanding phenomenon underlined by the use of the FFT is the emergence of an infinite number of spatial dispersion curves associated with each leaky wave propagating in shells when excited by a point source.

Phase gradient method applied to scattering by an elastic shell

We studied the resonances of an elastic cylindrical shell immersed in a fluid and filled with air with a new method based on the phase derivative of the scattering matrix with regard to the frequency. This method, derived from the Resonant Scattering Theory, enabled us to calculate with a good accuracy the resonance frequencies independently of the choice of a background. In the case of rather thin resonance widths, the background need not be taken into account to calculate the resonance widths. We show that the phase derivative with regard to the frequency is directly related to those derivatives with regard to the velocities which characterize wave propagation in the elastic shell and the fluids. This property is of interest when analyzing the sensitivity of the resonances related to elastic parameters. The phase derivatives with regard to the velocity of the wave in the surrounding fluid and the density of the shell allow us to characterize the coupling between the shell and the surrounding fluid. These last two derivatives are used to calculate the width of the resonances independently of the background in the cases when the coupling is not too large, that is to say for surface waves of the internal type.

Experimental analysis of phase spectrum of cylindrical or plane targets : a new global method of isolation of resonances

Abstract Up to now, resonance isolation by means of a pulse method has been performed by the calculation of the FFT of the free elastic response of the insonified target immersed in water. We propose a new method which allows the resonance detection from the FFT of the whole backscattered signal, involving the imaginary and real part spectra and in some cases, the phase spectrum. Experiments are carried out on several targets at normal incidence. This method seems to be the appropriate one to detect the resonances in the case of a “very absorptive material/elastic material” double layered plane structure.

The complex phase gradient method applied to leaky Lamb waves.

The classical phase gradient method applied to the characterization of the angular resonances of an immersed elastic plate, i.e., the angular poles of its reflection coefficient R, was proved to be efficient when their real parts are close to the real zeros of R and their imaginary parts are not too large compared to their real parts. This method consists of plotting the partial reflection coefficient phase derivative with respect to the sine of the incidence angle, considered as real, versus incidence angle. In the vicinity of a resonance, this curve exhibits a Breit-Wigner shape, whose minimum is located at the pole real part and whose amplitude is the inverse of its imaginary part. However, when the imaginary part is large, this method is not sufficiently accurate compared to the exact calculation of the complex angular root. An improvement of this method consists of plotting, in 3D, in the complex angle plane and at a given frequency, the angular phase derivative with respect to the real part of the sine of the incidence angle, considered as complex. When the angular pole is reached, the 3D curve shows a clear-cut transition whose position is easily obtained.

The radiation Q factors obtained from the partial derivatives of the phase of the reflection coefficient of an elastic plate

The phase gradient method is applied to study the partial derivatives of the phase of the reflection coefficient of a fluid-loaded elastic plate. We consider the derivatives with respect to the frequency f, the incidence angle theta, the phase velocities of the longitudinal and transverse waves propagating in the plate, cL and cT, respectively, and the phase velocity in the fluid cF. The partial derivatives with respect to f, cL, cT, cF are linked by a relation involving products of one of these variables with the corresponding partial derivative. At a resonance frequency, the product of frequency with the frequency phase derivative can be identified as a radiation quality factor. By analogy, the other products correspond to quality factors. It can be shown that the product assigned to the fluid phase velocity corresponds to an angular radiation quality factor. The products assigned to the longitudinal and transverse phase velocities are identified as longitudinal and transverse radiation quality factors. These quality factors are shown to be related to stored energies associated with either standing waves across the plate, guided waves, longitudinal waves or transverse waves. A reactive power balance between the plate and the fluid is also established.

The Im/Re spectrum method: A new method of detection of resonances of plane or cylindrical targets

The detection of resonances of various targets immersed in water is investigated by means of a new signal processing. The fast Fourier transform analysis of the reflected signal allows to obtain the evolution of the ratio between the imaginary part and the real part of the complex number obtained. This ratio strongly depends on the resonant character of the target. Special attention is given to the problem of the time origin in order to have a spectrum well interpretable in term of resonances. Results about a single plane plate, a coated plane plate and a solid cylinder are shown. The method proposed gives at least as much information as the classical ones in the case of an elastic target, and more information in the case of an elastic target coated with an absorbent.

The Im/Re method: A new experimental determination of resonances

The determination of resonances of elastic targets immersed in water has been performed by an impulsive method (A method). If one transducer is used alternatively as an emitter and as a receiver (monostatic method), the power spectrum of a part of the backscattered signal (i.e., the first echo have been omitted) by plates, solid cylinders, or pipes by an algorithm of fast Fourier transform (FFT) allow peaks that correspond to the resonances of the target to be isolated. In this paper a new method is proposed using the processing of the whole signal: The calculation of the FFT gives for each frequency a complex number. The ratio between the imaginary part and the real part of the complex number is plotted versus frequency: The Im/Re spectrum is obtained. When a resonance is excited, sharp transitions on the spectrum are observed. The reflected and transmitted signals by plates are studied. The cases of an aluminum plate and a PVC plate are investigated. The results are compared with those obtained by the A...