Geodesic
An approach to the analysis of propagation of elastic waves in grids made of rods of varying curvature
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 161 (2019) no. 3, pp. 365-376 Cet article a éte moissonné depuis la source Math-Net.Ru

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The influence of structural irregularity of lattice structures on the propagation of elastic waves in these structures was analyzed. The modeling was performed within the framework of solid body mechanics using the beam model of plane lattice structures. It was assumed that these structures are made of curvilinear elastic beams of varying curvature. Such structures can be made by additive manufacturing. The computations were performed by the finite-element method using the FIDESYS software. The propagation of waves was investigated for two types of lattice structures: elevator and star-shaped lattices. The results of computations show that the wave in these structures is propagated slower than in the classical structure with straight beams. The wave in the star-shaped lattice is propagated slower than in the elevator lattice. The results for the lattices with uniformly curved beams were compared with the results for the grids made of beams of varying curvature. The effect of wave frequency on the propagation of elastic waves in lattice structures was analyzed. The conceptual model of a device for wave frequency measuring was proposed for monochrome waves. The results can be used for design of filters, dampers of vibrations, and devices for wave frequency measuring.
Keywords: lattice structure, graded structures, elastic waves, additive manufacturing, finite-element method, frequency filtering of waves. 
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     title = {An approach to the analysis of propagation of elastic waves in grids made of rods of varying curvature},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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V. A. Levin; K. M. Zingerman; A. V. Vershinin; I. A. Podpruzhnikov. An approach to the analysis of propagation of elastic waves in grids made of rods of varying curvature. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 161 (2019) no. 3, pp. 365-376. http://geodesic.mathdoc.fr/item/UZKU_2019_161_3_a3/

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