Charles Croënne

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.

Tunable phononic crystals based on piezoelectric composites with 1-3 connectivity.

Phononic crystals made of piezoelectric composites with 1-3 connectivity are studied theoretically and experimentally. It is shown that they present Bragg band gaps that depend on the periodic electrical boundary conditions. These structures have improved properties compared to phononic crystals composed of bulk piezoelectric elements, especially the existence of larger band gaps and the fact that they do not require severe constraints on their aspect ratios. Experimental results present an overall agreement with the theoretical predictions and clearly show that the pass bands and stop bands of the device under study are easily tunable by only changing the electrical boundary conditions applied on each piezocomposite layer.

Brillouin scattering-like effect and non-reciprocal propagation of elastic waves due to spatio-temporal modulation of electrical boundary conditions in piezoelectric media

The properties of a one-dimensional phononic crystal made of identical piezoelectric elements separated by thin metallic electrodes connected to the ground are studied theoretically for cases where the locations of the electrical connections change as a function of time with a specific speed. This spatio-temporal modulation of the electrical boundary conditions results in significant non-linear effects that are evidenced numerically. The interaction between an incident harmonic longitudinal wave and the time-dependent phononic crystal is shown to lead to frequency splitting analogous to Brillouin scattering. Moreover, the boundaries of the Bragg bandgaps are strongly affected, and for some specific modulation speed, one-way wave propagation can be achieved.

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.

Control of elastic wave propagation in one-dimensional piezomagnetic phononic crystals.

Two ways of controlling the acoustic waves propagation by external inductance or capacitance in a one-dimensional (1-D) piezomagnetic phononic crystal are investigated. The structure is made of identical bars, constituted of a piezomagnetic material, surrounded by a coil and connected to an external impedance. A model of propagation of longitudinal elastic waves through the periodic structure is developed and the dispersion equation is obtained. Reflection and transmission coefficients are derived from a 2 × 2 transfer matrix formalism that also allows for the calculation of elastic effective parameters (density, Young modulus, speed of sound, impedance). The effect of shunting impedances is numerically investigated. The results reveal that a connected external inductance tunes the Bragg band gaps of the 1-D phononic crystal. When the elements are connected via a capacitance, a hybridization gap, due to the resonance of the LC circuit made of the piezomagnetic element and the capacitance, coexists with the Bragg band gap. The value of the external capacitance modifies the boundaries of both gaps. Calculation of the effective characteristics of the phononic crystal leads to an analysis of the physical mechanisms involved in the wave propagation. When periodically connected to external capacitances, a homogeneous piezomagnetic stack behaves as a dispersive tunable metamaterial.

Anomalous ultrasonic transport in phononic crystals with overlapping Bragg and hybridization gaps

Many of the interesting properties of phononic crystals are due to the existence of band gaps, which may arise from a number of different mechanisms. These include Bragg scattering as well as hybridization effects, the latter occurring when there are strong scattering resonances that hybridize with a propagating mode of the embedding medium. In this talk, we investigate the interaction between Bragg and hybridization effects on the band gap properties of 2D phononic crystals consisting of nylon rods arranged in a triangular lattice and immersed in water. The lattice constant and rod diameter were chosen to ensure that both mechanisms occur in the same frequency range. The scattering resonances of the nylon rods can be tuned in frequency by varying the temperature, enabling fine control of the overlap between hybridization and Bragg effects. The dispersion relations and transmission coefficient were measured experimentally from the phase and amplitude of transmitted ultrasonic pulses and calculated theoret...

Scattering from a finite ribbed plate with attached oscillators

Double layer structures consisting of stainless steel and polymer rods are designed to blur and attenuate Bragg and Bloch-Floquet scattering from a periodically ribbed plate in a given frequency bandwidth. These structures can be considered as ribbed plate-spring-mass systems, the resonance frequencies of which are obtained from random and circular permutations of five basic oscillators. Analytical and finite element methods are used to find their parameters and tank tests have been carried out to ensure the accuracy of the numerical results and validate the relevance of such a model. It has been found that the typical features associated with the periodicity of the ribs are replaced by a Christmas tree appearance when the far field pressure backscattered from the model is displayed in the (frequency, aspect angle) plane. An analysis of backscattering patterns is presented and comparisons with Naval Research Laboratory results are made.

Numerical and experimental demonstration of the Electrical Bragg band gaps in piezoelectric plates with a periodic array of electrodes

Recent analytical and numerical studies have shown that Electrical Bragg band gaps (EBBGs) may occur in piezoelectric plates poled along their thicknesses, with a 1D periodic array of electrodes on their two faces (Fig. 1) [C. Vasseur et al, Proceedings of 2016 IEEE IUS 2016, paper P3-C2-7, 4 pages]. These Bragg band gaps can be opened or closed by changing the electrical boundary conditions on the electrodes. In practice, the gap exists when all electrodes are left floating, and disappears when they are all grounded. In this paper, numerical and experimental results are presented for a finite piezoelectric plate and the concept is extended to a 2D periodic array of electrodes on the top and bottom surfaces of the piezoelectric plate, in order to control the propagation path of the wave.

Space-time modulation of electric boundary conditions in a one-dimensional piezoelectric phononic crystal

A phononic crystal constituted by a one-dimensional piezoelectric material with a periodic distribution of electrodes submitted to space and time-dependent electrical boundary conditions is considered in this work. Interaction of an incident elastic pulse propagating with such phononic crystal is studied using a specific Finite Difference Time Domain model. Simulations are conducted in the case of periodic grounded electrodes “moving” at constant subsonic or supersonic speed. Various nonlinear phenomena resulting from this interaction are observed: Brillouin-like acoustic scattering, non-reciprocity of transmission at fundamental frequency, parametric amplification of the incident wave. The dispersion curve of the wave propagating in the phononic crystal with space-time modulated electrical boundary conditions is also deduced from simulation results.

Focusing capability of a phononic crystal based on a hollow metallic structure

The dispersion curves of a phononic crystal (PC) based on a hollow metallic structure are presented. They exhibit a negative refraction dispersion branch and perfect refractive index matching with the surrounding water, leading to focusing capability. Numerical and experimental results are reported for a flat PC lens. The characteristics of the focal spot (intensity, dimensions, etc.) are numerically and experimentally investigated with the goal of finding the frequency of the optimal imaging performance.