Bruno Morvan

Experimental demonstration of the negative refraction of a transverse elastic wave in a two-dimensional solid phononic crystal

The negative refraction of transverse elastic waves is demonstrated experimentally in a two-dimensional phononic crystal (PC) made of a square lattice of cylindrical air cavities in an aluminum matrix. Dispersion curves of elastic waves in this PC exhibit a unique branch with phase and group velocities of opposite signs in a broad frequency range. Measurement of refraction angles through prismatic PC included in an aluminum block demonstrates negative refraction of elastic transverse wave.

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.

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.

Numerical analysis of negative refraction of transverse waves in an elastic material

A numerical analysis of negative refraction process is reported using a phononic crystal with an elastic solid matrix. The phononic crystal considered in this study is made of a periodic arrangement of holes in aluminum. Dispersion curves are discussed and conditions for which negative refraction can appear are identified. These conditions are obtained for the transverse waves, whereas the longitudinal waves are evanescent. A calculation is performed with a prism shaped phononic crystal, and it clearly exhibits a negative refraction angle. Several analyses are provided with a view to characterize the wave going out of the phononic crystal. Finally, improvements, with respect to the impedance matching and index tuning, are discussed.

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 ...

Experimental and numerical study of evanescent waves in the mini stopband of a 1D phononic crystal.

This paper deals with the analysis of the guided evanescent waves in stopbands of a 1D phononic crystal (PC). A new numerical implementation is shown in order to get the complex values of the wavenumbers in a frequency range where a gap occurs. The considered phononic system is an aluminum plate with a one-dimensional sinusoidal grating. For this structure a mode-gap (mini stopband) occurs at low frequency: it involves the two fundamental Lamb modes A(0) and S(0). The numerical study is performed by using a finite element method (ATILA code). The experiments deal with a finite length grating and evanescent waves are characterized at the vicinity of the mini stopband.

Analysis of elastic waves transmitted through a 2-D phononic crystal exhibiting negative refraction

A two-dimensional phononic crystal (PC) made of a square lattice of air holes in an aluminum matrix is studied. The band structure calculated in the irreducible Brillouin zone of the PC exhibits a branch with a negative slope that allows negative refraction. This phenomenon has been numerically verified using a prism-shaped PC for plane waves entering the PC with two different incidences. A detailed study of the waves at the exit of the PC shows that the plane wave is reconstructed after several wavelengths. Finally, the description of the refracted waves is interpreted using a point source array, giving information about the angular spreading and the relative amplitude of each refracted beam.

Negative refraction of elastic waves in 2D phononic crystals: Contribution of resonant transmissions to the construction of the image of a point source

Negative refraction properties of a two-dimensional phononic crystal (PC), made of a triangular lattice of steel rods embedded in epoxy are investigated both experimentally and numerically. First, experiments have been carried out on a prism shaped PC immersed in water. Then, for focusing purposes, a flat lens is considered and the construction of the image of a point source is analyzed in details, when indices are matched between the PC and the surrounding fluid medium, whereas acoustic impedances are mismatched. Optimal conditions for focusing longitudinal elastic waves by such PC flat lens are then discussed.

A multiple-scale perturbation approach to mode coupling in periodic plates

In this paper, guided ultrasonic wave propagation is analyzed in an elastic plate with sinusoidal surface corrugations. The corrugated area acts as a finite-length grating which corresponds to a 1-D phononic crystal (PC). The multiple-scale perturbation technique is used to derive coupled-mode equations describing the amplitudes of interacting modes. These equations are solved exactly for the two-point boundary-value problem of the PC. The study involves the coupling of the incident symmetric Lamb wave S0 to the reflected antisymmetric Lamb wave A0. The influences of the depth of corrugation and length of the PC are studied. Theoretical results are compared with experimental measurements.