An approach to the analysis of propagation of elastic waves in grids made of rods of varying curvature

V.A. Levin^a* , K.M. Zingerman^b** , A.V. Vershinin^a*** , I.A. Podpruzhnikov^a****
^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

Full text pdf

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).

References

1. Vendik I.B., Vendik O.G. Metamaterials and their application in ultrahigh-frequency engineering. Zh. Tekh. Fiz., 2013, vol. 83, no. 1, pp. 3–28. (In Russian)

2. Cheng L., Liang X., Bai J., Chen Q., Lemon J., To A. On utilizing topology optimization to design support structure to prevent residual stress induced build failure in laser powder bed metal additive manufacturing. Addit. Manuf., 2019, vol. 27, pp. 290–304. doi: 10.1016/j.addma.2019.03.001.

3. Trainiti G., Rimoli J.J., Ruzzene M. Wave propagation in undulated structural lattices. Int. J. Solids Struct., 2016, vol. 97–98, pp. 431–444. doi: 10.1016/j.ijsolstr.2016.07.006.

4. Fish J., Shek K. Multiscale analysis of composite materials and structures. Compos. Sci. Technol., 2000, vol. 60, nos. 12–13, pp. 2547–2556. doi: 10.1016/S0266-3538(00)00048-8.

5. Gibson L.J., Ashby M.F. Cellular Solids: Structure and Properties. Cambridge, Cambridge Univ. Press, 1997. 510 p.

6. Phani A.S., Woodhouse J., Fleck N. Wave propagation in two-dimensional periodic lattices. J. Acoust. Soc. Am., 2006, vol. 119, no. 4, pp. 1995–2005. doi: 10.1121/1.2179748.

7. Vasiliev A.A., Dmitriev S.V., Miroshnichenko A.E. Multi-field modeling of a Cosserat lattice: Models, wave filtering, and boundary effects. Eur. J. Mech. A/Solids, 2014, vol. 46, pp. 96–105. doi: 10.1016/j.euromechsol.2014.02.011.

8. Sedov L.I. Mekhanika sploshnoi sredy [Continuum Mechanics]. Vol. 2. Moscow, Nauka, 1970. 568 p. (In Russian)

9. Pobedrya B.E., Georgievskiy D.V. Osnovy mekhaniki sploshnoi sredy. Kurs lektsii [Fundamentals of Continuum Mechanics. A Course of Lectures]. Moscow, FIZMATLIT, 2006. 272 p. (In Russian)

10. Eglit M.E. Lektsii po mekhanike sploshnykh sred [Lectures on Continuum Mechanics]. Moscow, Izd. Mosk. Univ., 2008. 318 p. (In Russian)

11. Levin V.A., Vershinin A.V. Chislennye metody. Parallel'nye vychisleniya na EVM [Numerical Methods. Parallel Computing]. Vol. 2. Moscow, FIZMATLIT, 2015. 544 p. (In Russian)

12. Morozov E.M., Levin V.A., Vershinin A.V. Prochnostnoi analiz. Fidesis v rukakh inzhenera [Strength Analysis. Fidesys in the Hands of an Engineer]. Moscow, URSS, 2015. 408 p. (In Russian)

13. Levin V.A., Vershinin A.V. Industrial package for engineering strength analysis. XI Vseros. s'ezd po fundam. problemam teoret. i prikl. mekhaniki. Kazan', 20–24 avg. 2015 g. [Proc. XI All-Russ. Congress on Fundamental Problems of Theoretical and Applied Mechanics. Kazan, Aug. 20–24, 2015]. Kazan, Kazan. Univ., 2015, pp. 2281–2283. (In Russian)

14. Levin V.A., Vershinin A.V., Mishin I.A., Sboichakov A.M., Petrovskii K.A. Propagation of elastic waves in nonlinear media with initial strains. Computer modeling in CAE Fidesys. Tekhnol. Seismorazved., 2012, no. 4, pp. 29–32. (In Russian)

15. Levin V.A., Vershinin A.V. To modeling of elastic wave propagation in inhomogeneous media using parallel computing (CUDA technology). Materialy Mezhdunar. nauch. konf. ''Sovremennye problemy matematiki, mekhaniki, informatiki''. Tula, 23–27 noyab. 2009 g. [Proc. Int. Sci. Conf. ``Modern Problems of Mathematics, Mechanics, and Informatics''. Tula, Nov. 23–27, 2009]. Tula, TulGU, 2009, pp. 215–217. (In Russian)

16. Levin V.A., Vershinin A.V., Zingerman K.M. Numerical analysis of propagation of nonlinear waves in prestressed solids. Modern Appl. Sci., 2016, vol. 10, no. 4, pp. 158–167. doi: 10.5539/mas.v10n4p158.

17. Charara M., Vershinin A., Sabitov D., Pekar G. SEM wave propagation in complex media with tetrahedral to hexahedral mesh. Proc. 73rd Eur. Association of Geoscientists and Engineers Conf. and Exhib. Vienna, Austria, 2011, pp. 41–45.

18. CAE Fidesys. Available at: https://cae-fidesys.com/.

The content is available under the license Creative Commons Attribution 4.0 License.