DETERMINATION OF ELASTIC WAVE TRANSMISSION COEFFICIENT IN A METAMATERIAL WITH LATTICES OF DOUBLY-PERIODIC ELLIPTICAL CRACKS
DOI:
https://doi.org/10.15407/dopovidi2025.03.025Keywords:
periodic elliptical cracks, wave transmission coefficient, wave diffraction and interference, boundary integral equation method, wide-space model, mapping methodAbstract
The three-dimensional problem of propagation of harmonic longitudinal waves in an elastic solid containing double-periodic arrays of elliptical cracks located in a finite set of equidistant parallel square lattices is considered. In the frequency domain, a boundary integral equation for the reference crack opening in the unit cell of the double-periodic structure is obtained using the appropriate Green’s function. For the stability of numerical calculations, the Green’s function is represented in an exponentially convergent form, and its regularization is achieved by employing closed-form expressions for special lattice sums. The numerical solution of the equation is carried out using the mapping method. The wave transmission coefficient in a metamaterial with a single crack in the lattice is calculated by substituting the boundary element solutions into approximation relations for the wave field distant from the lattice. In the case of multiple lattices, this coefficient is determined based on a wide-space equidistant model of wave propagation.
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