Hybrid Numerical-Analytical Scheme for Calculating Elastic Wave Diffraction in Locally Inhomogeneous Waveguides

Глушков, Е. В.; Glushkova, N. V.; Евдокимов, А. А.

doi:10.1134/s1063771018010086

Cited by 14 publications

(6 citation statements)

References 19 publications

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“…This is illustrated by the example of frequency dependence of the transmission coefficient κ + = E + /E 0 ( Fig. 4) [6]. Here E + is the time-averaged wave energy transferred to infinity behind the obstacle by the field u + sc , and E 0 is the total time-averaged power supplied by the point source at x 0 = −5; the obstacle is of half-width a = 1, and the half-width of the FEM area D F is b = 10 for FEM-PML and b = 4 for FEM-An.…”

Section: Fem-an Verificationmentioning

confidence: 96%

“…The wavenumbers ζ n are roots of the characteristic (dispersion) equation for the waveguide considered, and the eigenforms a n are eigensolutions in the Fourier transform domain associated with these roots. Conventionally, they are calculated using the modal analysis technique, but we traditionally obtain them from the Green's matrix based integral representation of the force-generated solution in the intact waveguide [6]:…”

Section: Mathematical Frameworkmentioning

confidence: 99%

“…To use FEM, the values c ± n have to be already obtained, which is impossible before the values of u F and σ F are calculated. In addition, the FEM computation requires to specify only two functions on the border ∂D F out of four components of the vector-functions u sc and σ sc that appear in conditions (5) and (6). That is, the FEM problem is overdetermined, and to form the input data, one can only use either conditions (5) or (6).…”

Section: General Schemementioning

confidence: 99%

“…Applicability of the FEM-An scheme was first demonstrated with an analytically solvable test case [6]. The waveguide was taken in the form of a homogeneous elastic layer with a flexible but inextensible thin patch bonded to the surface (Fig.2).…”

Section: Fem-an Verificationmentioning

confidence: 99%

“…Nevertheless, we have developed a hybrid numerical-analytical scheme that uses standard FEM software only at the scatterers [6]. This scheme is based on the prior calculation of FEM solutions in the local subdomain with the boundary conditions induced by normal modes supported by the outer part of the waveguide.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid Numerical-Analytical Scheme for Locally Inhomogeneous Elastic Waveguides

Глушков¹,

Glushkova²,

Евдокимов³

2021

14th WCCM-ECCOMAS Congress

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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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Section: Fem-an Verificationmentioning

confidence: 96%

Section: Mathematical Frameworkmentioning

confidence: 99%