V.A. Levina* , K.M. Zingermanb** , A.V. Vershinina*** , I.A. Podpruzhnikova****
a Moscow State University, Moscow, 119991, Russia
b Tver State University, Tver, 170100, Russia
E-mail: *v.a.levin@mail.ru, **zingerman@rambler.ru, ***versh1984@mail.ru, ****ivanpodpr08@yandex.ru
Received May 28, 2019
DOI: 10.26907/2541-7746.2019.3.365-376
For citation: Levin V.A., Zingerman K.M., Vershinin A.V., Podpruzhnikov I.A. An approach to the analysis of propagation of elastic waves in grids made of rods of varying curvature. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2019, vol. 161, no. 3, pp. 365–376. doi: 10.26907/2541-7746.2019.3.365-376. (In Russian)
Abstract
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
Acknowledgments. The study was performed at Tula State Lev Tolstoy Pedagogical University and supported by the Ministry of Science and Higher Education of the Russian Federation (project no. 14.577.21.0271, project ID RFMEFI57717X0271).
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