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Vibrations of Periodic Systems Consisting of Identical Subsystems of an Arbitrary Structure

  • MECHANICS OF MACHINES
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Abstract

Vibrations and waves are investigated in periodic systems that consist of identical subsystems having an arbitrary structure. Spectral regularities are found for such systems. Their dispersion curves are shown to consist of branches, each of which corresponds to its own mode shape of elastic vibrations of the subsystem. The presence of band gaps in such systems, in which a harmonic signal cannot be transmitted, was revealed, and their boundaries were determined. The mode shapes of vibrations in various frequency ranges are obtained. Modulated waves are shown to arise in the system due to modulation by lower frequencies, which correspond to system vibrations without taking into account the elastic properties of the constituent subsystems.

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REFERENCES

  1. Vibratsii v tekhnike. Spravochnik (Vibrations in Engineering: Reference Book), Moscow: Mashinostroenie, 1980, vols. 3–4.

  2. Barmina, O.V. and Volokhovskaya, O.A., Methods of vibration analysis for multistage immersion pumps for oil extraction, Mashinostr. Inzh. Obraz., 2011, no. 1, pp. 7–17.

  3. Jung, J., Kim, H., Goo, S., Chang, K., and Wang, S., Realisation of a locally resonant metamaterial on the automobile panel structure to reduce noise radiation, Mech. Syst. Signal Process., 2019, vol. 122, pp. 206–231. https://doi.org/10.1016/j.ymssp.2018.11.050

    Article  Google Scholar 

  4. Qureshi, A., Li, B., and Tan, K., Numerical investigation of band gaps in 3D printed cantilever-in-mass metamaterials, Sci. Rep., 2016, vol. 6, no. 1. https://doi.org/10.1038/srep28314

  5. Bobrovnitskii, Yu.I., An acoustic metamaterial with unusual wave properties, Acoust. Phys., 2014, vol. 60, no. 4, pp. 371–378. https://doi.org/10.1134/s1063771014040010

    Article  Google Scholar 

  6. Huang, H.H., Sun, C.T., and Huang, G.L., On the negative effective mass density in acoustic metamaterials, Int. J. Eng. Sci., 2009, vol. 47, no. 4, pp. 610–617. https://doi.org/10.1016/j.ijengsci.2008.12.007

    Article  Google Scholar 

  7. Hu, G., Tang, L., Das, R., Gao, S., and Liu, H., Acoustic metamaterials with coupled local resonators for broadband vibration suppression, AIP Adv., 2017, vol. 7, no. 2, p. 025211. https://doi.org/10.1063/1.4977559

    Article  Google Scholar 

  8. Zhou, X., Wang, J., Wang, R., and Lin, J., Band gaps in grid structure with periodic local resonator subsystems, Mod. Phys. Lett. B, 2017, vol. 31, no. 25, p. 1750225. https://doi.org/10.1142/s0217984917502256

    Article  MathSciNet  Google Scholar 

  9. Banakh, L.Ya., Barmina, O.V., and Volokhovskaya, O.A., Oscillations and waves in multisection rotor systems, J. Mach. Manuf. Reliab., 2021, vol. 50, no. 5, pp. 396–404. https://doi.org/10.3103/S105261882105006X

    Article  Google Scholar 

  10. Kaluba, Ch. and Zingoni, A., Group-theoretic buckling analysis of symmetric plane frames, J. Struct. Eng., 2021, no. 10, p. 4021153. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003131

  11. Banakh, L.Ya., Propagation of elastic waves in dynamically self-similar structures (dynamic fractals), Acoust. Phys., 2020, vol. 66, no. 3, pp. 250–256. https://doi.org/10.1134/S1063771020020013

    Article  Google Scholar 

  12. Mencik, J. and Duhamel, D., Dynamic analysis of periodic structures and metamaterials via wave approaches and finite element procedures, Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2015), Athens, 2021, Papadrakakis, M. and Fragiadakis, M., Eds., Athens: Inst. of Structural Analysis and Antiseismic Research Natl. Technical Univ. of Athens, 2021, p. 42. https://doi.org/10.7712/120121.8462.19149

  13. Mandel’shtam, L.I., Lektsii po teorii kolebanii (Lecture Notes in Theory of Oscillations), Moscow: Nauka, 1972.

  14. Pain, H.J., The Physics of Vibrations and Waves, London: John Wiley & Sons, 1969, 2nd ed.

    Google Scholar 

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Funding

This study was supported by the Russian Science Foundation, project no. 21-19-00813.

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Authors and Affiliations

  1. Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, Russia

    L. Ya. Banakh

  2. Institute for Problems in Machine Building, Nizhny Novgorod, Russia

    L. Ya. Banakh & I. S. Pavlov

Authors
  1. L. Ya. Banakh
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  2. I. S. Pavlov
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Correspondence to L. Ya. Banakh.

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The authors declare that they have no conflicts of interests.

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Translated by M. Shmatikov

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Banakh, L.Y., Pavlov, I.S. Vibrations of Periodic Systems Consisting of Identical Subsystems of an Arbitrary Structure. J. Mach. Manuf. Reliab. 52, 293–300 (2023). https://doi.org/10.3103/S1052618823040052

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  • DOI: https://doi.org/10.3103/S1052618823040052

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