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Simulation of the Mechanical Wave Propagation in a Viscoelastic Media With and Without Stiff Inclusions

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Numerical Methods and Applications (NMA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13858))

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Abstract

The contribution focuses on the numerical simulation of wave propagation in an array of solid inclusions regularly distributed in a viscoelastic matrix. Waves are provoked by a transient load. The study aims to compare wave propagation in the viscoelastic continuum with and without the presence of solid inclusions. To this end, stress and displacement evolutions (in the time domain) are monitored at specified locations at the boundaries of the defined continuum. The case study contributes to a better understanding of the phenomena related to the reflection and diffraction of the mechanical waves by the solid inclusions. The modeled set-up often referred to in the literature as a phononic crystal, will possibly shed light on numerous practical applications. Among others, these are high sound absorption and strategies for the detection of defect locations.

Supported by the Russian Foundation for Basic Research (RFBR), project number 20-58-18002, and the Bulgarian National Science Fund, project number KP-06- Russia/5 from 11.12.2020.

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References

  1. Ivansson, S.M.: Sound absorption by viscoelastic coatings with periodically distributed cavities. J. Acoust. Soc. Am. 119(6), 3558–3567 (2006)

    Article  Google Scholar 

  2. Leroy, V., Strybulevych, A., Lanoy, M., Lemoult, F., Tourin, A., Page, J.H.: Superabsorption of acoustic waves with bubble metascreens. Phys. Rev. B 91(2), 020301 (2015)

    Article  Google Scholar 

  3. Liu, Z., et al.: Locally resonant sonic materials. Science 289(5485), 1734–1736 (2000)

    Article  Google Scholar 

  4. Duranteau, M., Valier-Brasier, T., Conoir, J.-M., Wunenburger, R.: Random acoustic metamaterial with a subwavelength dipolar resonance. J. Acoust. Soc. Am. 139(6), 3341–3352 (2016)

    Article  Google Scholar 

  5. Hinders, M., Rhodes, B., Fang, T.: Particle-loaded composites for acoustic anechoic coatings. J. Sound Vib. 185(2), 219–246 (1995)

    Article  MATH  Google Scholar 

  6. Ivansson, M.: Numerical design of Alberich anechoic coatings with superellipsoidal cavities of mixed sizes. J. Acoust. Soc. Am. 124(4), 1974–1984 (2008)

    Article  Google Scholar 

  7. Leroy, V., Bretagne, A., Fink, M., Willaime, H., Tabeling, P., Tourin, A.: Design and characterization of bubble phononic crystals. Appl. Phys. Lett. 95(17), 171904 (2009)

    Article  Google Scholar 

  8. Colombi, A., Roux, P., Guenneau, S., Gueguen, P., Craster, R.V.: Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances. Sci. Rep. 6(1), 1–7 (2016)

    Article  Google Scholar 

  9. Rozovskii, M.I. : The integral operator method in the hereditary theory of creep. Dokl. Akad. Nauk SSSR 160(4), 792–795 (1965)

    Google Scholar 

  10. Rabotnov, Y.N.: Elements of Hereditary Solid Mechanics. Naka Publishers, Moscow (1977). [in Russian]

    Google Scholar 

  11. Ilyasov, M.H.: Dynamical torsion of viscoelastic cone. TWMS J. Pure Appl. Math 2(2), 203–220 (2011)

    MathSciNet  MATH  Google Scholar 

  12. Jeltkov, V.I., Tolokonnikov, L.A., Khromova, N.G. : Transfer functions in viscoelastic body dynamics. Dokl. Akad. Nauk 329(6), 718–719 (1993)

    Google Scholar 

  13. Lychev, S.A.: Coupled dynamic thermoviscoelasticity problem. Mech. Solids 43(5), 769–784 (2008)

    Article  Google Scholar 

  14. Rossikhin, Y.A., Shitikova, M.V., Trung, P.T. : Analysis of the viscoelastic sphere impact against a viscoelastic Uflyand-Mindlin plate considering the extension of its middle surface. Shock Vibr. 2017, 5652023 (2017)

    Google Scholar 

  15. Mainardi, F.: Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models. Imperial College Press, London (2010)

    Book  MATH  Google Scholar 

  16. Achenbach, J.D.: Vibrations of a viscoelastic body. AIAA J. 5(6), 1213–1214 (1967)

    Article  Google Scholar 

  17. Colombaro, I., Giusti, A., Mainardi, F.: On the propagation of transient waves in a viscoelastic Bessel medium. Z. Angew. Math. Phys. 68(3), 1–13 (2017). https://doi.org/10.1007/s00033-017-0808-6

    Article  MathSciNet  MATH  Google Scholar 

  18. Christensen, R.M.: Theory of Viscoelasticity: An Introduction. Academic Press, New York (1982)

    Google Scholar 

  19. Zheng, Y., Zhou, F.: Using Laplace transform to solve the viscoelastic wave problems in the dynamic material property tests. In EPJ Web Conf. 94, 04021 (2017)

    Article  Google Scholar 

  20. Igumnov, L.A., Korovaytseva, E.A., Pshenichnov, S.G.: Dynamics, strength of materials and durability in multiscale mechanics. In: dell’Isola, F., Igumnov, L. (eds.) Advanced Structured Materials, ASM, vol. 137, pp. 89–96. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-53755-5

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Acknowledgments

This study was performed within the bilateral project funded by the Russian Foundation for Basic Research (RFBR), project number 20-58-18002, and by the Bulgarian National Science Fund, project number KP-06-Russia/5 from 11.XII.2020.

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Authors and Affiliations

  1. Technical University of Sofia, 8, Kliment Ohridski boulevard, Sofia, Bulgaria

    Todor Zhelyazov

  2. Institute of Mechanics, Lomonosov Moscow State University, Michurinsky prospect 1, Moscow, 119192, Russia

    Sergey Pshenichnov

Authors
  1. Todor Zhelyazov
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  2. Sergey Pshenichnov
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Correspondence to Todor Zhelyazov .

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Editors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Georgiev

  2. Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Maria Datcheva

  3. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir Georgiev

  4. Sofia University “St. Kliment Ohridski”, Sofia, Bulgaria

    Geno Nikolov

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Zhelyazov, T., Pshenichnov, S. (2023). Simulation of the Mechanical Wave Propagation in a Viscoelastic Media With and Without Stiff Inclusions. In: Georgiev, I., Datcheva, M., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2022. Lecture Notes in Computer Science, vol 13858. Springer, Cham. https://doi.org/10.1007/978-3-031-32412-3_30

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  • DOI: https://doi.org/10.1007/978-3-031-32412-3_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-32411-6

  • Online ISBN: 978-3-031-32412-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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