ISSN 2347-3487 Volume 11, Number 7 Journalof Advances in Physics 3564 | Page council for Innovative Research April 2016 www.cirworld.com The efficiency of application of virtual cross-sections method and hypotheses MELS in problems of wave signal propagation in elastic waveguides with rough surfaces A. S. Avetisyan, А. А. Hunanyan Institute of Mechanics, National Academy of Sciences, Yerevan, Republic of Armenia ara.serg.avetisyan@gmail.com hunanyan.areg21@gmail.com ABSTRACT The efficiency of virtual cross sections method and MELS (Magneto Elastic Layered Systems) hypotheses application is shown on model problem about distribution of wave field in thin surface layers of waveguide when plane wave signal is propagating in it. The impact of surface non-smoothness on characteristics of propagation of high-frequency horizontally polarized wave signal in isotropic elastic half-space is studied. It is shown that the non-smoothness leads to strong distortion of the wave signal over the waveguide thickness and along wave signal propagation direction as well. Numerical comparative analysis of change in amplitude and phase characteristics of obtained wave fields against roughness of weakly inhomogeneous surface of homogeneous elastic half-space surface is done by classical method and by proposed approach for different kind of non-smoothness. Indexing terms/Keywords Rough surface - Cross sections method - Surface geometric heterogeneities - Weakly inhomogeneous surface - Hypothesis-MELS - Modelling of boundary value problems Academic Discipline And Sub-Disciplines Mechanics of Deformable Solids, Mathematics in Engineering SUBJECT CLASSIFICATION Applied Mathematics and Physics TYPE (METHOD/APPROACH) The use of combinated method 1 INTRODUCTION It is known that unlike Rayleigh wave it is impossible the localization of horizontally polarized (SH) waves near perfectly smooth mechanically free surface of isotropic elastic half-space [1,2]. From the other hand side, there exist localized high- frequency (short) waves near the contact line between elastic half-space and thin mechanically soft layer made from different material (see for example [2]). The localization of high frequency wave signals at smooth free from mechanical loads surface of waveguide also occurs in the presence of certain physical properties of material of the half-space (see for example [3,8, 9]). The case of smooth surfaces, unlike non-smooth ones, being idealized models can almost always be completely investigated. It is especially important for investigation of high-frequency wave signals (short waves) propagation in layered waveguides considering the actual heterogeneity (non-smoothness) of the surface layers, especially when the length of the wave signal is proportional to average surface roughness step. Accounting inhomogeneous surface layers of the layered waveguide significantly complicates the study of mathematical model of the problem, but makes it possible to reveal new near-surface wave effects and more accurately calculate the quantitative characteristics of the wave field. Most theoretical investigations of acoustic problems for not-smooth surfaces are done either by appropriate integral transformation [5,6] or by a perturbation method [7], deriving asymptotic estimates of wave characteristics. In [19,20] SH acoustic waves propagation in plate with rough surface is studied by method of integral transformations assuming that the average roughness height everywhere is a small part of the thickness of the waveguides (plates). In [8] the influence of dispersion due to roughness on surface acoustic waves and wave packets (in the frequency range of 30-200 MHz) for different degrees of nano-meter roughness on the surface of silicon (section-001) and (section- 111) is investigated. It is shown that the effect of the frequency dispersion induced by surface roughness will be significant for some relative characteristics of non-smooth surfaces. Previously unknown dispersion effects caused by crystalline anisotropy of surface layers is revealed. In [9] the problem of Love waves propagation in corrugated isotropic layer of homogeneous isotropic halfspace studied. The dispersion relation for the corrugated layer is derived as a function of wave amplitude, frequency and parameters of the corrugated section. In particular cases, the dispersion relation has been studied for corrugated layers bounded by periodic surfaces d1 · cos(px) and d2 · cos(px). It should be noted also that in problems with complex statement about distribution of directed waves in waveguides, along with roughness of surfaces of the waveguide the reasons for arising new wave phenomena can be others (optical, electromagnetic, adhesive properties of bonded interfaces, etc.) [15, 16,21–24]. In some studies the boundary value problems are solved numerically often relying on algorithms involving finite element method on the basis of existing packages [25,26]. Such an approach of