Surface waves in materials with functionally gradient coatings

Abstract

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 repre sented as a convolution of the Green's matrix of the medium with the vector of surface stresses, while the trav eling surface waves are described by the residues from the poles of the Green's matrix Fourier symbol. Com parison 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 occur ring in micro and nanocoatings due to diffusions or technological features of sputtering and gluing of pro tective films.

Moving Load on an Elastic Half-Space Coated With a Thin Vertically Inhomogeneous Layer

“…Let us concentrate on the analysis of equation 15on the interface x 3 = 0. Note that on setting h = 0 the problem formulation (14), (15) will reduce to that for an uncoated elastic half-space which is the leading order Taylor expansion of the exact solution [6], for more details see [18].…”

“…More realistic modelling motivates development of studies oriented to dynamics of multi-layered and vertically inhomogeneous half-space, see e.g. [15] and [22].…”

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

“…The present paper is a continuation of the previous research [2] on the dispersion and amplitude properties of guided waves (GW) generated by a surface source in elastic half-spaces covered by various coatings. Among them, only coatings with soft inter-layers (internal channels [3]) demonstrated the effect of wave amplitude localization in certain frequency ranges for each specific GW.…”

“…The algorithms of K calculation are described in [2] and papers cited therein. The Fourier transform parameters α 1 and α 2 are replaced in Eq.…”

Hybrid Numerical-Analytical Scheme for Locally Inhomogeneous Elastic Waveguides

“…This way of obtaining expansion (2) is more convenient for us because we have elaborated and computer implemented a series of fast and numerically stable algorithms of matrix K calculation for multilayered, functionally graded, anisotropic, porous, cylindrical, and other elastic wavequides (e.g., [7][8][9]). Thus, the described below hybrid scheme FEM-An can be implemented for all such waveguides.…”