Philippe Gatignol

Theoretical analysis for the reflection of a focused ultrasonic beam from a fluid–solid interface

A theoretical study of the reflection of focused acoustic beams from a fluid–solid interface is presented. The incident field is defined by a Gaussian velocity distribution along a plane emitter. The reflected field is described through its pressure field in a region not restricted to the interface. Nonspecular phenomena were exhibited at any angle of incidence by means of short wave asymptotic analysis. In particular, for incidence near the Rayleigh angle, a distortion of a part of the caustic of the reflected beam including lateral and axial displacements of the focal point is observed.

Deviation of a monochromatic Lamb wave beam in anisotropic multilayered media: asymptotic analysis, numerical and experimental results

The aim of this paper is threefold: to describe the physical phenomenon of the excitation of modal waves such as Lamb waves, in anisotropic multilayered media, by a monochromatic incident beam, using an asymptotic approach; to present a three-dimensional model using the decomposition of the incident beam into monochromatic plane waves (the formalism is applied to the particle displacement vector); to illustrate the phenomenon both numerically and experimentally. Numerical and experimental maps of the reflected field of pressure are presented, and the reradiation of the Lamb wave beam in an oblique plane is theoretically and numerically illustrated.

Experimental study of focused ultrasonic beams reflected at a fluid-solid interface in the neighborhood of the Rayleigh angle

A technique for measuring the lateral and axial displacements of the focal point of an acoustic focused beam reflected at a water-aluminum interface in the neighborhood of the Rayleigh angle incidence is presented together with a qualitative representation of other nonspecular phenomena, based on the cartography of the reflected beam. A study of the feasibility of the experiment and the choice of the transducer is carried out. The results obtained are in agreement with theoretical predictions.<<ETX>>

Ultrasonic Field of a Transducer behind a Plane Fluid-Solid Interface

Ultrasonic echography is one of the methods which are more and more used for non destructive evaluation of materials, according to the requirements of the users who are often increasingly concerned by quantitative evaluation of defects. This requires a better knowledge of the measurement system, as well as of the ultrasonic field generated by the transducer inside of the material and this has led us to develop methods for the calculation of this field. We present a method for the determination of the ultrasonic field in a solid medium separated by a fluid-solid plane interface, from the knowledge, by modelization or by measures, of the field in a plane of the fluid medium. The method is based upon a decomposition by a plane waves obtained by spatial Fourier Transform, which permits a simple use of the SNELL-DESCARTES refraction laws at the interface. The method has shown quite good agreement with experimental results. Moreover, this method has permit us to predict undesirable effects in the case of oblique incident beams.

Analytical approach of Lamb waves coupling in rough isotropic plates

The present work aims at contributing to the investigation of an analytical method to describe Lamb waves which undergoes Lamb waves coupling when propagating along the rough surfaces of finite extent of isotropic, solid, and infinite plates. The motions considered are assumed to be independent of one of the coordinates for which the component of the displacement is equal to zero (two-dimensional problem). In some respect, the analytical approach is an extension of an analytical model describing the coupling of SH waves due to ridges (on the surface of a plate) parallel to the polarization of the waves, but it is treated in a somewhat different manner because the acoustic field involves here both the longitudinal and the transversal displacements of the Lamb waves. The formalism relies on an integral formulation, using Green’s functions which permit to express Lamb waves perturbations, to describe the coupling process between the longitudinal and the transversal components of the forward and the backward ...

Interaction of a monochromatic ultrasonic beam with a finite length defect at the interface between two anisotropic layers: kirchhoff approximation and fourier representation

This paper presents a fast computation method to simulate the interaction between a bounded acoustic beam and a 2-layered anisotropic structure with a finite defect on the internal interface. The method uses the classical Fourier decomposition of the fields into plane waves, and the Kirchhoff approximation is introduced to calculate the diffusion by the defect. The validity of the approximation is estimated by comparison with the Keller Geometrical Theory of Diffraction and with results obtained by boundary element methods. The quickness of the method allows testing several geometrical configurations (varying incident angle, thickness of the layers or the physical nature of the defect). These studies may be used to foresee what experimental configurations would be adequate to have a chance to detect the defect.

An Iterative Method for the Interaction Between a Bounded Beam and an Interface Defect in Solids, Under Kirchhoff Approximation

The method of passive re-emission under Kirchhoff approximation is used in this paper in order to solve the problem of the interaction of a monochromatic ultrasonic bounded beam (emitted by a plane transducer) with a bi-dimensional structure fluid/solid/solid which includes a plane defect located at the plane interface separating the two solids (assumed to be isotropic). The ultrasonic beam is decomposed into plane waves, using Fourier transforms. The presence of both the interfaces and the defect produces successive reflections. In order to take into account all the corresponding fields, an iterative method has been implemented. At each iteration, the problem of the scattering by the defect is processed with the passive re- emission method, the data on the defect being calculated under Kirchhoff approximation (in good agreement with the Geometrical Theory of Diffraction for a defect located in a fluid medium); the transmission through the interfaces is performed for plane waves, the scattered field being expressed using Fourier integrals. This iterative method gives a more accurate solution than the global one, namely the passive re-emission principle under Kirchhoff approximation straightforwardly applied on the whole system of the structure. Numerical results are given (cartographies and cuts of the pressure field in the fluid), which show -i) the effect of the defect on the field which propagates in the structure, -ii) the convergence rate of the iterative process as a function of the incident angle, -iii) the changes in the field depending on the location of the defect.

Deviation of the modal waves excited by an ultrasonic monochromatic beam in an anisotropic layer

Abstract The aim of the Note is to describe the physical phenomenon of the excitation of modal waves, such as Lamb waves, in anisotropic media by a monochromatic incident beam, and to explain the deviation of the modal wave beam so created. Using a stationary phase approach, the modal wave beam is found to be deviated in the direction normal to the modal slowness curve. Due to the anisotropy, this direction is no longer in the sagittal plane.

A stationary phase argument for the modal wave beam deviation in the time–space domain for anisotropic multilayered media

The aim of the paper is to describe the physical phenomenon of the excitation of modal waves, such as Lamb waves, in anisotropic multilayered media by a monochromatic incident beam and then by a time depending signal. A modal beam is generated in the structure and, due to the anisotropy of the media constituting the structure, is deviated with respect to the sagittal plane of the incident bounded beam. Using a stationary phase approach, it is possible to determine the deviation direction of the modal beam in the far field at a given frequency. This direction is normal to the modal curve, at the point corresponding to the main modal wave vector. Using Lagrange multipliers, it is possible to obtain the equation of an oblique plane in which the modal beam reradiates in the external fluid. As the modal waves are dispersive, the group velocity and the direction of propagation of the principal modal wave vary with the frequency. So, in the far field, for a time depending signal, the different monochromatic components of the main modal wave are found in different directions. In general, the main crest line of this modal wave packet is not a straight line.

Modal waves in periodically multilayered fluid structures

This paper aims to study the existence of modal waves and in particular of surface waves, in periodically multilayered fluid media. Generally speaking, these waves are propagation modes for which the acoustical energy propagates along the layers, whereas it remains bounded in a direction perpendicular to the layers. Periodically multilayered media are here studied by the transfer matrix method. The calculus of eigenvalues of the transfer matrix for one period permits to distinguish between passing and stopping regions in the wave number/frequency plane. The transfer matrix for a finite number of periods can be calculated by using Tchebychef polynomials. The writing of the boundary conditions for a finite structure surrounded by vacuum leads to a factorized equation. Thus, two families of guided waves are obtained: the first one corresponds to structure modes which exist in passing regions only. The second one only depends on the period properties and corresponds to inhomogeneous Floquet waves. When the pe...