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 parti… Show more
“…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].…”
Section: Analysis On the Interfacementioning
confidence: 99%
“…More realistic modelling motivates development of studies oriented to dynamics of multi-layered and vertically inhomogeneous half-space, see e.g. [15] and [22].…”
“…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].…”
Section: Analysis On the Interfacementioning
confidence: 99%
“…More realistic modelling motivates development of studies oriented to dynamics of multi-layered and vertically inhomogeneous half-space, see e.g. [15] and [22].…”
“…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.…”
Section: Introductionmentioning
confidence: 84%
“…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.…”
Section: Statement and Solution Of The Problemmentioning
The paper is focused on the source energy distribution in vertically inhomogeneous elastic halfspaces with soft internal channels. The analysis is performed using the Fourier transform technique and Green's matrix integral representations. Timeaveraged 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.
“…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.…”
Numerical simulation of guided wave excitation, propagation, and diffraction in laminate structures with local inhomogeneities (obstacles) is associated with high computational cost due to the need for a mesh-based approximation of extended domains with a rigorous account for the radiation conditions at infinity. To obtain computationally efficient solutions, hybrid numerical-analytical approaches are currently being developed, based on linking a numerical solution in a local vicinity of the source and/or obstacles with an explicit analytical representation in the external semi-infinite domain. However, the developed methods are generally not widely spread because the possibility of such coupling with an external multimode wave field is generally not provided in standard finite-element (FE) software. We propose a scheme that allows the use of the FE software as a black box for the required correct matching of local numerical and global analytical solutions (FEM-An). The FEM is used to obtain a set of local numerical solutions that serve as a basis in the inner domain. These solutions satisfy the boundary conditions induced by guided wave modes so that they fit correctly with the modal expansion in the outer region. The expansion coefficients of both FE and modal decompositions are determined then from the condition of stress and displacement continuity at the interface between the inner and outer domains. This scheme was numerically validated against analytical solutions to test problems and FE solutions for long waveguide sections with perfect match layer absorbing conditions at the ends (FEM-PML). Along the way, it turned out that the FEM-PML approach gives an incorrect result in the backward-wave bands and at high frequencies. The application of the FEM-An hybrid scheme is illustrated by examples of Lamb wave diffraction by elastic inclusions and delaminations.
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