Maxime Bavencoffe

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.

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.

Characterization of evanescent ultrasonic waves in a band gap of a 1D phononic crystal

This work deals with the propagation of Lamb waves on a plate engraved by a 1D periodic grating. Dispersion curves of the modes exhibit pass bands and stop bands. The aim of this work is to establish a link between the attenuation of the ultrasonic waves observed in the case of a limited grating and the values of the imaginary part of the wave number in a stop band computed for an infinite grating.

A comparison of 1D analytical model and 3D Finite Element Analysis with experiments for a Rosen-type piezoelectric transformer

This article is dedicated to the study of Piezoelectric Transformers (PTs), which offer promising solutions to the increasing need for integrated power electronics modules within autonomous systems. The advantages offered by such transformers include: immunity to electromagnetic disturbances; ease of miniaturisation for example, using conventional micro fabrication processes; and enhanced performance in terms of voltage gain and power efficiency. Central to the adequate description of such transformers is the need for complex analytical modeling tools, especially if one is attempting to include combined contributions due to (i) mechanical phenomena owing to the different propagation modes which differ at the primary and secondary sides of the PT; and (ii) electrical phenomena such as the voltage gain and power efficiency, which depend on the electrical load. The present work demonstrates an original one-dimensional (1D) analytical model, dedicated to a Rosen-type PT and simulation results are successively compared against that of a three-dimensional (3D) Finite Element Analysis (COMSOL Multiphysics software) and experimental results. The Rosen-type PT studied here is based on a single layer soft PZT (P191) with corresponding dimensions 18 mm × 3 mm × 1.5 mm, which operated at the second harmonic of 176 kHz. Detailed simulational and experimental results show that the presented 1D model predicts experimental measurements to within less than 10% error of the voltage gain at the second and third resonance frequency modes. Adjustment of the analytical model parameters is found to decrease errors relative to experimental voltage gain to within 1%, whilst a 2.5% error on the output admittance magnitude at the second resonance mode were obtained. Relying on the unique assumption of one-dimensionality, the present analytical model appears as a useful tool for Rosen-type PT design and behavior understanding.

Negative refraction of longitudinal waves in an elastic phononic crystal

Two-dimensional phononic crystals (PC) with square or triangular lattices composed of steel rods in a polymer matrix are studied. The band structure of the PC exhibits several negative branches. Among them, one allows the negative refraction of longitudinal waves transmitted through the PC. The left-handed behaviour of the PC is exhibited numerically as well as experimentally, by using a prism shaped PC. Finally, a numerical simulation is presented, with the PC immersed in a fluid, for focusing applications.

Development of a suitable PML for an harmonic study of a finite 1D phononic crystal

This paper deals with the interaction of ultrasonic Lamb waves with a 1D phononic crystal. The studied structure is a finite plate with a periodic corrugated surface. Two types of forbidden bands arise in the Lamb wave dispersion curves. The first one is located at the limit of the first Brillouin zone, the second one exists at the crossing of dispersion curves of two different Lamb modes. These forbidden bands lead to conversion phenomena. In order to study accuratly the conversion phenomena in the band gaps, harmonic finite element analysis are performed. Perfect matching layers (PML) on both sides of the plate are then necessary to avoid stationnary waves. PML, adapted for Lamb modes involved at a given frequency, must be designed. By using these PML, the attenuation of Lamb waves propagating in the phononic crystal is clearly shown and is related to the existence of the forbidden band.

Decoherence of lamb waves by rough interface

Propagation of Lamb waves in elastic plate with a periodic grating on one interface has shown an attenuation which can be interpreted as a phenomenon of decoherence. In order to verify this hypothesis, a simplified model is considered, where a fluid plate with a limited periodic grating on one interface is studied by the finite element method (ATILA). An antisymmetric Lamb mode is excited before the grating. The pressure is studied under the grating along the median plane of the plate, where it is equal to zero for the homogeneous plate. In the general case, when the wavelength of the Lamb wave is close to the grating spacing, reflected waves are observed and a phonon relation is written between the incident signal, the converted mode and the phonon related to the grating. The pressure in the median plane is particularly studied if the phonon relation is verified or not. A. Homogeneous fluid plate In this section, an homogeneous fluid plate is considered. Its thickness T is 5 mm. Its density is 2700 kg/m 3 and its wave velocity VF is 6320 m/s. It corresponds to a fictive fluid which properties are close to aluminium, in order to explain previous observations made with an elastic rough plate (3). The equations of the dispersion curves (4) can be obtained by writing the propagation of waves in the plate and using the boundary conditions at the surfaces ± T/2. The wave number of the propagating modes are given by: