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- W4386875488 abstract "We consider the scattering of in-plane waves that interact with an edge of a structured inertial line defect contained in a triangular lattice, composed of periodically placed masses interconnected by massless elastic rods. The steady state problem is converted into a vector Wiener-Hopf equation using Fourier transform. The matrix Wiener-Hopf kernel of this equation describes all dynamic phenomena engaged in the scattering process, which includes instances where localised interfacial waves can emerge along structured defect. This information is exploited to identify the dependency of the existence of these waves on the incident wave parameters and properties of the inertial defect. The symmetry in the structure of scattering medium allows us to convert the vectorial problem into a pair of scalar Wiener-Hopf equations posed along the lattice row containing the defect. Their solution enables the exact representation of scattered field, in terms of a contour integral in the complex plane, that includes the contributions of evanescent and propagating waves. The solution reveals the decomposition of remote lattice response into a linear combination of terms from three distinct symmetry classes. These classes correspond to tensile modes acting transverse to the defected lattice row, shear modes that act parallel to this row, and wave modes represented as a mixture of these two responses. Benchmark finite element calculations are provided to validate results based on the obtained solution, which involve numerical computations of the contour integrals. Graphical illustrations demonstrate special dynamic responses encountered during the wave scattering process, including dynamic anisotropy, negative reflection and negative refraction." @default.
- W4386875488 created "2023-09-20" @default.
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- W4386875488 date "2023-09-17" @default.
- W4386875488 modified "2023-09-27" @default.
- W4386875488 title "Scattering of lattice waves by an inertial line defect in planar motion" @default.
- W4386875488 doi "https://doi.org/10.48550/arxiv.2309.09286" @default.
- W4386875488 hasPublicationYear "2023" @default.
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