The dispersion of waves in a system of elastic rods periodically supported with flexible elements

Authors

  • V.N. Oliynik Institute of Hydromechanics of the NAS of Ukraine, Kiev

DOI:

https://doi.org/10.15407/dopovidi2017.08.027

Keywords:

bending vibrations, dispersion, Floquet method, periodic elastic structure, phase velocity

Abstract

Wave properties of a periodic structure formed by two parallel infinite rods reinforced by periodically placed simply supported flexible bars are studied. In the cases of in-phase and anti-phase longitudinal motions of the rods, the dispersion equations are obtained by the Floquet method, and phase velocity values are determined for a harmonic wave propagating in the considered system. A significant dispersion is shown to be inherent to this wave due to exciting the bending modes of the bars in the corresponding frequency ranges.

Downloads

References

Brillouin, L. & Parodi, M. (1946) Wave propagation in periodic structures. New York: Dover.

Brekhovskikh, L. M. (1973) Waves in layered media, Moscow: Nauka (in Russian).

Silin, R. A. (2006). Electromagnetic waves in artificial periodic structures. Uspekhi Fiz. Nauk, 175, pp. 562-565 (in Russian). https://doi.org/10.3367/UFNr.0176.200605j.0562

Heckl, M. A. (1964). Investigations on the vibrations of grillages and other simple beam structures. J. Acoust. Soc. Am., 36, No. 7, pp. 1335-1343. https://doi.org/10.1121/1.1919206

Oliynik, V. N. (2015). On the dispersion of waves of some types in pulmonary parenchyma. Visn. Taras Shevchenko Nat. Univ of Kyiv. Ser. Phys.-Math. Sci., Special iss., pp. 189-192 (in Ukrainian).

Mead, D. J. (1970). Free wave propagation in periodically supported, infinite beams. J. Sound Vib., 11, No. 2, pp. 181-197. https://doi.org/10.1016/S0022-460X(70)80062-1

Oliynik, V. N. (2008). Wave propagation in the system of two parallel rods periodically supported by rigid transverse barriers and connected with an acoustic medium. Akust. Visn., 11, No. 1, pp. 60-67 (in Ukrainian).

Oliynik, V. N. (2008). Antisymmetric waves in the system of two parallel rods periodically supported by rigid transverse barriers and connected with an acoustic medium. Akust. Visn., 11, No. 2, pp. 36-44 (in Ukrainian).

Downloads

Published

15.09.2024

How to Cite

Oliynik, V. (2024). The dispersion of waves in a system of elastic rods periodically supported with flexible elements . Reports of the National Academy of Sciences of Ukraine, (8), 27–33. https://doi.org/10.15407/dopovidi2017.08.027

Issue

No. 8 (2017): Reports of the National Academy of Sciences of Ukraine

Section

Mechanics

License

Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.