Catherine Potel

Propagation in an anisotropic periodically multilayered medium

An anisotropic multilayered medium is studied using the method of transfer matrices, developed by Thomson [J. Appl. Phys. 21, 89 (1950)] and Haskell [Bull. Seismol. Soc. Am. 43, 17 (1953)]. The propagation equations in each layer of the multilayered medium use the form developed by Rokhlin et al. [J. Acoust. Soc. Am. 79, 906–918 (1986); J. Appl. Phys. 59 (11), 3672–3677 (1986)]. Physical explanations are given, notably when a layer is made up of a monoclinic crystal system medium. The displacement amplitudes of the waves in one layer may be expressed as a function of those in another layer using a propagation matrix form, which is equivalent to relating the displacement stresses of a layer to those in another layer. An anisotropic periodically multilayered medium is then studied by using a propagation matrix that has particular properties: a determinant equal to one and eigenvalues corresponding to the propagation of the Floquet waves. An example of such a medium with the axis of symmetry of each layer perpendicular to the interfaces is then presented together with the associated reflection coefficients as a function of the frequency or of the incident angle.

Characterization of composite materials by ultrasonic methods: modelization and application to impact damage

This paper presents some ultrasonic methods to detect and to characterize defects, possibly obtained after damage caused in composite materials. Firstly, a two-dimensional ultrasonic cartography, performed section by section, at different positions from the impact point, allows the participation of the delamination mechanisms which took part through the thickness of a pultruded glass fiber-reinforced plastic composite beam, to be analyzed. A very good agreement has been found with destructive testings. Furthermore, some examples are given on the use of an ultrasonic propagation model which has been developed. This model permits optimum experimental configurations to be determined, by the use of transmission and reflection coefficients or of Lamb waves. In addition, experimental and modelized time signals have been compared.

Acoustic propagation in anisotropic periodically multilayered media: A method to solve numerical instabilities

Acoustic propagation through thick composites has become a subject of intensive study due to their application to nondestructive evaluation. The anisotropic multilayered media are now usually studied by the propagator matrix formalism. Though this formalism is very convenient, it leads to numerical instabilities for thick composites at high frequencies. These numerical instabilities come from the combination of very high exponential terms which reduces the dynamics of the calculation. A very interesting case is the one of anisotropic periodically multilayered media. The method developed in this paper uses Floquet waves which correspond to the modes of an infinite periodically multilayered medium. They are linear combinations of the real waves propagating in each layer of the medium. The Floquet wave numbers are the eigenvalues of the propagation matrix of one period of the medium. The anisotropic periodically multilayered medium can then be considered as a dummy medium in which the Floquet waves propagate...

Floquet waves and classical plane waves in an anisotropic periodically multilayered medium: Application to the validity domain of homogenization

The aim of this paper is to better understand the correspondence between classical plane waves propagating in each layer of an anisotropic periodically multilayered medium and Floquet waves. The last are linear combinations of the classical plane waves. Their wave number is obtained from the eigenvalues of the transfer matrix of one cell of the medium. A Floquet polarization which varies with its position in the periodically multilayered medium has been defined. This allows one to define a Floquet wave displacement by analogy with the displacement of classical plane waves, and to check the equality of the two displacements at any interface separating two layers. The periodically multilayered medium is then an equivalent material, considered as homogeneous, and one can draw dispersion curves and slowness surfaces which are dispersive. In the low‐frequency range, when the relation between the Floquet wave numbers and the frequency is linear, the multilayered medium can be homogenized; the Floquet polarizati...

Importance of the near Lamb mode imaging of multilayered composite plates

In recent years Lamb waves are being used for internal defect detection in multilayered composite plates. Different Lamb modes generate various stress levels in different layers. As a result, all Lamb modes are not equally sensitive to internal defects of various layers. A number of studies have been carried out to identify which Lamb mode is most effective for detecting defects in a specific layer. However, one shortcoming of the Lamb wave inspection technique is that in a symmetrically layered composite plate stress and displacement magnitudes and energy distribution profiles for all Lamb modes are symmetric about the central plane of the plate. As a result, the ability of a Lamb mode to detect defects in a specific layer of the plate is identical to its ability to detect defects in the corresponding layer of mirror symmetry. Hence, from the Lamb wave generated image one cannot distinguish between the defects in these two layers of mirror symmetry. In this paper it is investigated how by fine-tuning the frequency and the striking angle of the incident beam in the neighborhood of a Lamb mode one can separately detect internal defects in layers of mirror symmetry in the upper and lower halves of a plate.

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...

Lamb wave attenuation in a rough plate. II. Analytical and numerical results in a fluid plate

This paper aims at providing analytical and numerical approaches to analyze the behavior of guided waves (Lamb-type waves) propagating inside plates with a rough surface considered here as distributed small perturbations. A physical interpretation of the attenuation phenomenon of the propagating mode generated by the source (mode coupling) is provided for an ideal rough plate (fluid plate) using an analytical model available in the literature. This analytical model is validated using a numerical method. The obtained results on periodically corrugated surfaces of fluid plates emphasize the role played by the spatial period and the modal coupling. They serve also as results for interpreting the effect due to randomly rough surfaces in solid plates, notably the effect of the power spectrum density of the rough profile (including the effect of the statistical roughness parameters mentioned in Part I). The results obtained experimentally and theoretically, for the attenuation factor of the main Lamb wave, are ...

On the modeling of modes coupling in dissipative fluid-filled waveguide with corrugated surfaces

This paper aims at providing an alternative analytical model, which would be more suitable than a previous one [C. Potel and M. Bruneau, J. Sound Vib. 313, 738 (2008)], to describe the mode coupling due to scattering on small one-dimensional irregularities (parallel ridges) of the surfaces of a fluid-filled waveguide. Both models rely on standard integral formulation and modal analysis, the acoustic field being expressed as a coupling between eigenmodes of a regularly shaped waveguide, which bounds outwardly the corrugated waveguide considered. But the model presented here departs from the previous one essentially because it starts from the integral formulation for the acoustic pressure field, the solution relying on a modal expansion, whereas the previous one starts from the inner product of the set of differential equations (which govern the acoustic pressure field) and the appropriate eigenfunctions, the solution being obtained from using a one-dimensional integral formulation. Substituting this altern...

Modes coupling of shear acoustic waves polarized along a one-dimensional corrugation on the surfaces of an isotropic solid plate

This paper aims at providing an analytical model, suitable to highlight the mode coupling due to scattering on small one-dimensional irregularities (parallel ridges) of the surfaces of isotropic solid plates, when shear horizontal waves polarized along the ridges propagate perpendicularly to them. An impedancelike boundary condition at the interface between the teeth (the ridges) and the inner plate (bounded outwardly by the ridges) accounts for the inertia of the teeth to describe the roughness. Using the integral formulation, the displacement field is expressed as a coupling between eigenmodes of the inner regular-shaped plate.

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.