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

Oliynik, VN
Dopov. Nac. akad. nauk Ukr. 2017, 8:27-33
https://doi.org/10.15407/dopovidi2017.08.027
Section: Mechanics
Language: Ukrainian
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.

Keywords: bending vibrations, dispersion, Floquet method, periodic elastic structure, phase velocity
References: 
  1. Brillouin, L. & Parodi, M. (1946) Wave propagation in periodic structures. New York: Dover.
  2. Brekhovskikh, L. M. (1973) Waves in layered media, Moscow: Nauka (in Russian).
  3. 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
  4. 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
  5. 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).
  6. 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
  7. 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).
  8. 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).