Sergey I. Fomenko

Influence of porosity on characteristics of rayleigh-type waves in multilayered half-space

Poroelastic fluid-saturated multilayered half-space is considered; particle motion in this half-space is described by Biot-Frenkel equations for two-phase media. A brief description of the derivation of integral and asymptotic representations for wave fields excited by a given surface load is presented; the influence of the porous microstructure on the form of dispersion curves and amplitude characteristics of excited traveling waves is analyzed. It is demonstrated using numerical examples that the amplitude of additional modes occurring due to the presence of a microstructure can be essentially larger than the amplitudes of principal modes present in the waveguide with purely elastic layers.

Surface waves in materials with functionally gradient coatings

Surface wave excitation and propagation in a half-space with a continuous dependence of elastic properties on depth has been considered. The total wave field generated by a given surface load can be represented as a convolution of the Green’s matrix of the medium with the vector of surface stresses, while the traveling surface waves are described by the residues from the poles of the Green’s matrix Fourier symbol. Comparison of the gradient and multilayer models shows that with a high enough number of partitions (layers), the dispersion properties and amplitude-frequency characteristics of surface waves in FGMs are described by the curves obtained upon a steplike approximation of gradient properties; however, with high contrast properties, the multilayer model can be more time-consuming. The effect of the vertical inhomogeneity of the medium on the surface wave characteristics has been analyzed for a series of typical dependences occurring in micro- and nanocoatings due to diffusions or technological features of sputtering and gluing of protective films.

Wave energy transfer in elastic half-spaces with soft interlayers.

The paper deals with guided waves generated by a surface load in a coated elastic half-space. The analysis is based on the explicit integral and asymptotic expressions derived in terms of Greens matrix and given loads for both laminate and functionally graded substrates. To perform the energy analysis, explicit expressions for the time-averaged amount of energy transferred in the time-harmonic wave field by every excited guided or body wave through horizontal planes and lateral cylindrical surfaces have been also derived. The study is focused on the peculiarities of wave energy transmission in substrates with soft interlayers that serve as internal channels for the excited guided waves. The notable features of the source energy partitioning in such media are the domination of a single emerging mode in each consecutive frequency subrange and the appearance of reverse energy fluxes at certain frequencies. These effects as well as modal and spatial distribution of the wave energy coming from the source into the substructure are numerically analyzed and discussed.

Elastic Wave Propagation in Anisotropic and Functionally Graded Layered Phononic Crystals: Band-Gaps, Pass-Bands and Low Transmission Pass-Bands

This paper describes a mathematical model of plane wave propagation in anisotropic and functionally graded layered phononic crystals with finite and infinite number of unit-cells. Classification of pass-bands and band-gaps is presented based on asymptotic analysis of the wave-fields in periodic layered structures. Two kinds of band-gaps where the transmission coefficient decays exponentially with the number of unit-cells are specified. The so-called low transmission pass-bands are introduced in order to identify frequency ranges in which the transmission is low enough for engineering applications, but it does not tend to zero exponentially with the number of unit-cells approaching infinity. The results of the numerical simulation are presented in order to demonstrate wave propagation phenomena. The influence of the anisotropy and functionally graded interlayers on the band-gaps and pass-bands is analysed.

Simulation of plane 3D wave propagation in layered piezoelectric phononic crystals

Plane wave propagation in layered piezoelectric phononic crystals is considered. The wavefields are calculated in terms of the transfer matrix method providing a sustainable solution through the exploitation of T-matrix in Jordan form. Representation based on eigenvalues of transfer matrix leads to numerical stability, it allows estimation of wave energy transmission coefficients for analysis of filtration properties. The results of parametric studies of elastic wave propagation in piezoelectric phononic crystal are presented.

Wave motion in piezoelectric layered phononic crystals with and without electroded surfaces

Plane wave excitation and propagation in layered piezoelectric phononic crystals with and without given electric potentials at the metallic interfaces is studied in the present work. Two kinds of piezoelectric layered phononic crystals are considered: an infinite periodic structure and a periodic structure surrounded by two half-spaces. The influences of electrodes on wave transmission, band-gaps and pass-bands are investigated.

Band-gaps and low transmission pass-bands in layered piezoelectric phononic crystals

In-plane wave propagation in layered piezoelectric phononic crystals composed of functionally graded interlayers arisen from the solid diffusion is considered in the present work. Wave transmission and band-gaps due to the material gradation and incident wave-field are investigated. A classification of band-gaps in layered piezoelectric functionally graded phononic crystals is proposed. The classification relies on the analysis of the eigenvalues of the transfer matrix for a unit-cell and the asymptotics derived for the transmission coefficient. The so-called low transmission pass-bands are introduced in order to identify frequency ranges, in which the wave transmission is sufficiently low for engineering applications, but it does not tend to zero exponentially as the number of the unit-cells tends to infinity. Wave-fields, low transmission pass-bands and band-gaps in layered and functionally graded piezoelectric phononic crystals are analyzed.

Source energy distribution and successive forwarding in layered and functionally graded elastic substructures

The paper is focused on the source energy distribution in vertically inhomogeneous elastic half-spaces with soft internal channels. The analysis is performed using the Fourier transform technique and Greens matrix integral representations. Time-averaged wave energy fluxes are calculated based on the Umov-Poynting energy vector concept. The excited guided waves exhibit a peculiar effect of wave energy localization in certain, specific for each wave mode, frequency ranges. Outwardly, it looks like a successive energy forwarding from every current mode to the next one.