Bulk longitudinal wave reflection/transmission in periodic piezoelectric structures with metallized interfaces

A theoretical study is performed of the bulk acoustic wave propagation in periodic piezoelectric structures with metallized interperiod boundaries. A crucial specific feature of such structures is that the bounded acoustic beam incident perpendicular to an interface can generate scattered (i.e. reflected and transmitted) waves over the whole area of the interface rather than only within the spot where this acoustic beam crosses the interface as it occurs in the absence of metallization. This extra generation is due to the electric potential which is induced by the incident wave on the whole metallized boundary rather than only on its part. The expressions are obtained for the reflection and transmission coefficients in the case where a longitudinal wave propagates along the 6-fold symmetry axis of a hexagonal piezoelectric. The periodicity is realized by inserting thin metallic layers (electrodes) into otherwise homogeneous material perpendicular to its 6-fold axis. The derived expressions allow the determination of the amplitude of waves arising both inside and outside the incident acoustic beam. The analysis of these expressions shows that the extra generation in question is able to significantly alter the distribution of the wave amplitudes as compared with the pattern which is obtained without taking into account the wave fields appearing outside the domain occupied by the incident acoustic beam.

Synthesis of bio-inspired multilayer polarizers and their application to anti-counterfeiting

Some insects, such as Papilio blumei and Suneve coronata, are known for exhibiting polarization effects on light such as color contrast or geometrical polarization rotation by reflection on their wing scales. The photonic structures found on these species that show these properties are multilayered spherical cavities or triangular grooves which polarize the light due to multiple inner reflections. These polarization effects, in addition to the intrinsic color-mixing properties of these photonic structures, are of interest in the anti-counterfeiting field due to their invisibility to the naked eye. In this paper, we report micro-fabrication techniques to produce bio-inspired cylindrical grooves (C-grooves) and triangular grooves (V-grooves) that demonstrate the same properties. Theoretical analyses were carried out by using multi-scale simulation (MS) as well as by finite-difference time-domain (FDTD) in order to compare the polarization capability of both structures. The V-grooves show greater polarization contrast than the C-grooves, but the spectrum is specular. The C-grooves exhibit lower polarization effects but have a dispersive spectrum. In both cases, the structures show additional optical properties, such as diffraction, macroscopic color contrast under a polarizer, and contrast inversion due to geometries which contribute to their uniqueness.

Tunable effective constants of the one-dimensional piezoelectric phononic crystal with internal connected electrodes

One-dimensional propagation of a longitudinal wave through an infinite piezoelectric periodically layered structure is considered. The unit cell consists, in general, of piezoelectric multilayers separated by thin electrodes which are connected through a capacitor with capacity Cj that plays the role of the external electric control providing tunability of the mechanical properties. The main focus of the present study is on the effective properties characterizing the homogenized medium. Due to the electric boundary conditions, the 4×4 transfer matrix M through the period T can be reduced to 2 × 2 dimension governing the mechanical fields only. As a result, the homogenized medium is pure elastic though its effective material parameters depend on the piezoelectric and dielectric coefficients of the actual piezoelectric medium, as well as on Cj. The effective parameters and the impedance in the low-frequency limit ω→0 and at finite frequency are obtained and analyzed.

Liquid Crystal Templating Effects on Silica Gels Synthesized using Quaternary Ammonium Surfactants

The use of lyotropic liquid crystal phases is a promising tool in tailoring the porous structure of inorganic gels. In this work, we examine the effect of hexagonal liquid crystal phases produced with quaternary ammonium surfactants on the textural ordering of silica gels.

The sol-gel polymerization of the silicon alkoxide precursor (tetramethoxysilane) is followed by 29Si NMR and rheological measurements. The structural evolution of the material from the starting sol to the thermally treated gel is studied using low angle X-ray diffraction. The textural characteristics of the gels are correlated with the nature of the surfactant molecules.

On-Line Spectroscopic Studies of Group iv Alkoxides and their Interactions with Polymerizable Organic Additives During the Sol-Gel Process

The monitoring of different reactions such as the stabilization of the alkoxides with polymerizable organic additives, the building of the inorganic network during the hydrolysis process, and in a same manner, the polymerization of the organic additives, can be of great importance for the development of hybrid materials with improved processability.

NIR spectroscopy is a very versatile technique but lacks of specificity. IR and Raman give more interpretative results but are not always easy to run on a process. We used both techniques along with chemometric tools to extract relevant information from our processes. Then 2D correlation allowed to benefit from the specificity of IR and Raman to develop robust NIR methods able to be used on line to control the different steps of the sol-gel process.

The hydrolysis of mixed species of titanium containing chloro, isopropoxo and methacrylato ligands will be discussed in terms of mechanism occuring during the sol-gel process.

Effective Willis constitutive equations for periodically stratified anisotropic elastic media

A method to derive homogeneous effective constitutive equations for periodically layered elastic media is proposed. The crucial and novel idea underlying the procedure is that the coefficients of the dynamic effective medium can be associated with the matrix logarithm of the propagator over a unit period. The effective homogeneous equations are shown to have the structure of a Willis material, characterized by anisotropic inertia and coupling between momentum and strain, in addition to effective elastic constants. Expressions are presented for the Willis material parameters which are formally valid at any frequency and horizontal wavenumber as long as the matrix logarithm is well defined. The general theory is exemplified for scalar SH motion. Low frequency, long wavelength expansions of the effective material parameters are also developed using a Magnus series, and explicit estimates are derived for the rate of convergence.

Existence and spectral properties of shear horizontal surface acoustic waves in vertically periodic half-spaces

The paper is concerned with the propagation of shear horizontal surface waves (SHSW) in semi-infinite elastic media with vertically periodic continuous and/or discrete variation of material properties. The existence and spectral properties of the SHSW are shown to be intimately related to the shape of the properties variation profile. Generally, the SHSW dispersion branches represent randomly broken spectral intervals on the ( ω ,  k ) plane. They may, however, display a particular regularity in being confined to certain distinct ranges of slowness s = ω / k , which can be predicted and estimated directly from the profile shape. The SHSW spectral regularity is especially prominent when the material properties at the opposite edge points of a period are different. In particular, a unit cell can be arranged so that the SHSW exists within a single slowness window, narrow in the measure of material contrast between the edges, and does not exist elsewhere or vice versa. Explicit analysis in the ( ω ,  k ) domain is complemented and verified through the numerical simulation of the SH wave field in the time–space domain. The results also apply to a longitudinally periodic semi-infinite strip with a homogeneous boundary condition at the faces.

Trapping of shear acoustic waves by a near-surface distribution of cavities

For a halfspace containing random and uniform distribution of empty cylindrical cavities within finite depth beneath the surface, the dispersion spectrum of coherent shear horizontal waves is calculated and analyzed based on the effective-medium approach. The scattering-induced dispersion and attenuation are coupled with the effect of a surface waveguide filled with scatterers. As a result, the obtained spectrum bears certain essential particularities in comparison with the standard Love-wave pattern. Simple analytical estimates enable a direct evaluation of the concentration of scatterers from the dispersion data.

Intermittent Brownian dynamics over a rigid strand: heavily tailed relocation statistics in a simple geometry

We analyze the intermittent Brownian dynamics (a succession of adsorption and bulk relocation steps) of a test particle over a single strand. We propose an analytic expression of the relocation time distribution at all times. We show that this distribution has a nontrivial heavily tailed statistics at long time with a diverging average relocation time. In order to experimentally probe this first passage statistics, we follow the intermittent Brownian dynamics of water molecules over long and stiff imogolite mineral strands, using a field cycling NMR dispersion technique. Our analytic derivation is found to be in good agreement with experimental data on a large domain of observation. Implications for the efficiency of a search strategy on a single filament are then discussed and the importance of the confinement and/or the finite size effect is emphasized.

Inhomogeneous plane wave and the most energetic complex ray

This paper presents a study on the wave surfaces of anisotropic solids. In addition to the classical and real rays, which are defined by the normal to the slowness surfaces, it is obtained complex rays, which are associated to specific inhomogeneous plane waves. Referring to the complex Christoffel's equation and to the Fermat's principle, an intrinsic equation can be associated to these complex rays. Limiting the study to principal planes and plotting the associated complex wave surfaces, it can be shown that four energetic rays always exist in any directions for both quasi-isotropic and anisotropic media (even beyond the cusp). Consequently, it is always possible to define four closed wave surfaces (real or not).

Surface acoustic waves at the vacuum-thermoviscoelastic solid interface

The present investigation concerns the propagation of surface waves at the vacuum-solid interface of a solid which is isotropic and thermoviscoelastic, i.e., for which the effects of heat conductivity need to be taken into account. Calculations show that, in addition to the Rayleigh wave, a thermal surface wave propagates that couples both the thermal and the elasticity effects. This latter wave is interpreted in terms of evanescent plane waves. The displacement field associated with this wave is calculated and interpreted. Some experimental results are also presented.

Transient Lamb waves: comparison between theory and experiment

This paper presents an experimental investigation of the generation of transient Lamb waves inside an immersed plate by a time limited signal. The transient Lamb waves are the solutions of the characteristic equation of the plate for complex frequency and real slowness, in contrast to the leaky Lamb waves, for which the slowness is complex and the frequency is real. By using a large transducer in agreement with the real slowness assumption, the excitation of these transient Lamb waves is observed experimentally both in reflection and transmission for a tone burst excitation. Particular attention is paid to the A0 mode for which the amplitude increases exponentially in time. As a result, the total reflected waveform contains in this case a transient contribution, coming from the generation of the A0 mode, that precedes the forced regime. It is shown that there is a very good agreement between the theoretical and the experimental time exponential amplitude variations of the transient Lamb waves. For the A0 mode, the transient signal is qualitatively explained by a group velocity higher than the phase velocity.