Anne-Christine Hladky-Hennion

Tunable magnetoelastic phononic crystals

The feasibility of tuning the band structure of phononic crystals is demonstrated by employing magnetostrictive materials and applying an external magnetic field. Band structures are calculated with a plane wave expansion method that accounts for coupling between the elastic behavior and the magnetic field through the development of elastic, piezomagnetic, and magnetic permeability effective tensors. We show the contactless tunability of the absolute band gaps of a two-dimensional phononic crystal composed of an epoxy matrix and Terfenol-D inclusions. The tunable phononic crystal behaves like a transmission switch for elastic waves when the magnitude of an applied magnetic field crosses a threshold.

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.

Negative refraction of acoustic waves using a foam-like metallic structure

A phononic crystal (PC) slab made of a single metallic phase is shown, theoretically and experimentally, to display perfect negative index matching and focusing capability when surrounded with water. The proposed PC slab is a centimeter scale hollow metallic foam-like structure in which acoustic energy is mediated via the metal lattice. The negative index property arises from an isolated branch of the dispersion curves corresponding to a mode that can be coupled to incident acoustic waves in surrounding water. This band also intercepts the water sound line at a frequency in the ultrasonic range. The metallic structure is consequently a candidate for the negative refraction of incident longitudinal waves.

Band structures tunability of bulk 2D phononic crystals made of magneto-elastic materials

The feasibility of contactless tunability of the band structure of two-dimensional phononic crystals is demonstrated by employing magnetostrictive materials and applying an external magnetic field. The influence of the amplitude and of the orientation with respect to the inclusion axis of the applied magnetic field are studied in details. Applications to tunable selective frequency filters with switching functionnality and to reconfigurable wave-guides and demultiplexing devices are then discussed.

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.

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.

Experimental validation of band gaps and localization in a one-dimensional diatomic phononic crystal

The propagation of compressional ultrasonic pulses through a finite one-dimensional chain of various unit cells is investigated experimentally. The chain, initially compressed by an axially applied constant force, is excited by a periodic force, which acts in line with axis of bead chain. The experimental measurements giving the eigenfrequencies of the specimen are based on a Fourier analysis of the transmitted acoustic pulse. The results are compared with the numerical calculations and it is shown that the two approaches are well correlated. A phononic band structure is observed and under certain conditions, depending on the parity of the number and on the masses of the beads in the chain, it is shown that localized modes propagating in the forbidden band are exhibited. Much attention is devoted to the existence of these localized modes according to the mass ratio between two adjacent beads constituting the unit cell.

Numerical homogenization techniques applied to piezoelectric composites

With the recent availability of piezoelectric fibers, the design and the analysis of piezoelectric composites needs new modeling tools. Therefore, a numerical homogenization technique has been developed, based on the ATILA finite element code, that combines two techniques: one relying upon the representative volume element (RVE) the other relying upon the wave propagation (WP). The combination of the two methods allows the whole tensor of the homogenized properties of the piezoelectric composite to be found. Considering a fiber embedded in epoxy, the numerical results are compared to the results obtained using previous analytical models, thus validating the models. Even if the method is presented in a particular case, its extension to any piezoelectric composite is straightforward.

Attenuation of lamb waves in the vicinity of a forbidden band in a phononic crystal

When a Lamb wave propagates on a plate engraved by a periodic grating, it may exhibit attenuation. This attenuation is related to a coupling of this incident mode with other propagating modes. As the propagation takes place in a periodic medium, the dispersion curves of the modes are of interest because they exhibit passbands and stopbands related to the geometry of the waveguide. The goal of this work is to quantitatively establish the relation between the value of the attenuation of the propagating waves and the width of the forbidden bands appearing inside the Brillouin zone. This study is performed by using a finite element method (ATILA code).

Lamb waves in phononic crystal slabs with square or rectangular symmetries

We report on both numerical and experimental results showing the occurrence of band gaps for Lamb waves propagating in phononic crystal plates. The structures are made of centered rectangular and square arrays of holes drilled in a silicon plate. A supercell plane wave expansion method is used to calculate the band structures and to predict the position and the magnitude of the gaps. The band structures of phononic crystal slabs are then measured using a laser ultrasonic technique. Lamb waves in the megahertz range and with wave vectors ranging over more than the first two reduced Brillouin zones are investigated.