Pascal Rembert

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...

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.

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...

The short pulse method of isolation and identification of resonances : comparison with a quasiharmonic method and application to axisymmetrical scatterers

Several experimental methods using quasiharmonic insonification lead to a direct verification of the resonance scattering theory. They provide, for elastic cylindrical targets, the resonance frequencies and the mode number of each of them. Pulsed techniques already existing only allowed the resonance frequency determination. Recently, a short pulse method of isolation and identification of resonances (short pulse MIIR) has been initiated. It completes previous works and allows a complete comparison with theoretical and quasiharmonic experimental results. This method consists in digitizing the time signals that characterize the scattering from an elastic target insonified by a short pulse for different angular positions of the receiving transducer. For each acquired signal a resonance spectrum is obtained after a spectral amplitude analysis. From these data, computer processing allows the plotting of identification patterns and by the same way the knowledge of the mode of vibration at a given resonance fre...

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.

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.

The Wigner-Smith matrix in acoustic scattering: Application to fluid-loaded elastic plates

The Wigner-Smith matrix Q is built up by differentiation of the unitary condition of the scattering matrix S. The matrices Q and S both contain the same information but with different points of view. For structures with simple geometrical shapes such as plates or cavities, the acoustic scattering is a two channel scattering represented by a 2×2 S matrix. The elements of the Q matrix can be described: (i) by means of the phase derivatives of the elements of the matrix S, (ii) by means of the phase derivatives of the eigenvalues of the S matrix. The equivalence of these two descriptions allows one to express the phase derivatives of (i) in terms of the phase derivatives of (ii). The Wigner-Smith matrix concept enables one to unify and to improve both the phase gradient method and the eigenvalue method in the frame of the multichannel scattering. It obviously incorporates the resonance scattering theory. Approximate resonant formulas and numerical results are given for the case of fluid loaded elastic isotro...

Submerged plane layered isotropic media: Properties of the scattering matrix eigenvalues with application to bilayers (L)

The plot of the transmission coefficient moduli cannot be used to analyze all the resonances of layered structures because of the overlapping of the resonances. A method using the scattering matrix eigenvalues is presented. It allows, first, to annihilate the overlapping and to recover the resonance positions and half-widths and second, to divide in two independent sets most of the resonances involved in symmetric structures as well as in nonsymmetric ones. Comparisons between the results provided by the method and those coming from the poles of the transmission coefficient agree. In many cases, the transition terms constitute a generalization of the transmission coefficients.

Methods of Isolation of Modal Resonances

The scattering problem by immersed targets involves the resonance phenomenon. Different methods of isolation of modal resonances are discussed: the Resonant Scattering Theory (the different backgrounds used in this method are considered), the phase gradient method (which is partly independent of the background choice), and the Argand diagram method (leading to both theoretical and experimental determination of the frequency and the width of resonances) and an exact description of the resonance components of partial modes (involving the determination of the roots of the characteristic equation in the complex frequency plane). The results provided by these methods are compared, their validity domain is discussed. Whatever the method, the resonant components appear as Breit-Wigner functions: this is the common point between the different methods. This review article includes 119 references.

Methods of isolation of modal resonances (a review).

The analytical methods of isolation and description of the resonance components of partial modes in scattering problems of acoustic, elastic, and electromagnetic waves are set forth. The results of these methods’ applications are presented and their effectiveness is discussed. For some particular cases the exactness of the results obtained can be estimated as well. The following methods are considered: gradient of the phase, utilization of impedance type intermediate backgrounds, Argand diagram method, and pole evaluation on the frequency complex plane for a fixed mode order. The methods can be even used for rather complicated situations: for very narrow and rather broad resonances, near the point of intersection of the dispersion curves of phase velocities, and for very close situated resonances. The illustrative examples are given for the problems of scattering of bodies of spherical and cylindrical shape. The resonances are isolated for waves of different physical nature: diffracted (Franz type), norma...