Peculiarities of flexural wave propagation in a notched bar

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The results of numerical modeling and experimental studies of the propagation of flexural elastic waves in a metal notched bar approximates the effect of an acoustic black hole are presented. The sample is a bar with notches, the depth of which increases according to the power law with an exponent equal to (4/3). It has been confirmed experimentally and with the simulation results, that such bars slow down the propagation of an elastic wave to the end of the bar. It is shown in such structures flexural waves have dispersion and their localization at the end of the bar is higher for some natural frequencies than that of a solid rod. The natural oscillations of the whole and notched bars are compared, i.e. the shape of the amplitude of the flexural wave along the rods. The dependence of the flexural wave length in a notched bar on the frequency is investigated as a wave propagates to the end of the bar.

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作者简介

A. Agafonov

Moscow State University named after M.V. Lomonosov

Email: aikor42@mail.ru

Faculty of Physics

俄罗斯联邦, Leninskie Gory, Moscow, 119991

M. Izosimova

Moscow State University named after M.V. Lomonosov

Email: aikor42@mail.ru

Faculty of Physics

俄罗斯联邦, Leninskie Gory, Moscow, 119991

R. Zhostkov

Institute of Physics of the Earth named after O.Yu. Schmidt RAS

Email: aikor42@mail.ru
俄罗斯联邦, Gruzinskaya st. 10, building 1, Moscow, 123995

A. Kokshayskiy

Moscow State University named after M.V. Lomonosov

Email: aikor42@mail.ru

Faculty of Physics

俄罗斯联邦, Leninskie Gory, Moscow, 119991

A. Korobov

Moscow State University named after M.V. Lomonosov

编辑信件的主要联系方式.
Email: aikor42@mail.ru

Faculty of Physics

 

俄罗斯联邦, Leninskie Gory, Moscow, 119991

N. Odina

Moscow State University named after M.V. Lomonosov

Email: aikor42@mail.ru

Faculty of Physics

俄罗斯联邦, Leninskie Gory, Moscow, 119991

参考

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  2. Krylov V.V., Shuvalov A.L. Propagation of localised flexural vibrations along plate edges described by a power law // Proc. of the Institute of Acoustics. 2000. V. 22. № 2. P. 263–270.
  3. Krylov V.V. Localized acoustic modes of a quadratic solid wedge // Moscow University Physics Bulletin. 1990. V. 45. №. 6. P. 65–69.
  4. Krylov V.V., Tilman F.J.B.S. Acoustic ‘black holes’ for flexural waves as effective vibration dampers // J. Sound Vib. 2004. V. 274. № 3−5. P. 605–619.
  5. Pelat A., Gautiera F., Conlon S.C., Semperlotti F. The acoustic black hole: A review of theory and applications // J. Sound Vib. 2020. V. 476. P. 115316.
  6. Guasch O., Arnela M., Sánchez-Martín P. Transfer matrices to characterize linear and quadratic acoustic black holes in duct terminations // J. Sound Vib. 2017. V. 395. P. 65–79.
  7. Krylov V.V. Acoustic black holes: recent developments in the theory and applications // IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2014. V. 61. № 8. P. 1296–1306.
  8. Bayod J.J. Experimental study of vibration damping in a modified elastic wedge of power-law profile // J. Vibr. Acoust. 2011. V. 133. № 6. P. 061003.
  9. Ji H., Luo J., Qiu J., Cheng L. Investigations on flexural wave propagation and attenuation in a modified one-dimensional acoustic black hole using a laser excitation technique // Mechanical Systems and Signal Processing. V. 104. 2018. P. 19−35.
  10. O’Boy D.J., Krylov V.V. and Kralovic V. Damping of flexural vibrations in rectangular plates using the acoustic black hole effect // J. Sound Vib. 2010. V. 329. P. 4672–4688.
  11. Агафонов А.А., Коробов А.И., Изосимова М.Ю., Кокшайский А.И., Одина Н.И. Особенности распространения волн Лэмба в клине из АБС пластика с параболическим профилем // Акуст. журн. 2022. Т. 68. № 5. С. 467–474.
  12. Миронов М.А. Точные решения уравнения поперечных колебаний стержня со специальным законом изменения поперечного сечения // Акуст. журн. 2017. Т. 63. № 5. С. 3–8.
  13. Миронов М.А. Точные решения уравнения поперечных колебаний стержня со специальным законом изменения поперечного сечения вдоль его оси // IX Всесоюзная акустическая конференция. 1991. Секция Л. С. 23–26.
  14. Миронов М.А. Разрезной стержень как вибрационная черная дыра // Акуст. журн. 2019. Т. 65. № 6. C. 736–739.

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2. Fig. 1. Diagram of the profile of a split rod.

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3. Fig. 2. (a) — Example of the specified geometry of the sample and (b) — finite element mesh.

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4. Fig. 3. Examples of bending vibration shapes of rods in horizontal projection: in the control sample at a frequency of (a) 12.8, (b) 22.7, (c) 54.6, (d) 99.9 kHz; and in the split rod at a frequency of: (d) 10.4, (e) 21.8, (g) 52.9, (h) 99.5 kHz.

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5. Fig. 4. Dispersion curves of a rod without cuts (the error of the experimentally obtained data is less than the marker value and increases from 2% to 9% with decreasing speed).

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6. Fig. 5. Distribution of the amplitude of the bending mode in a split rod.

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7. Fig. 6. (a) — Natural frequencies of the flexural mode propagating in the cut and control samples. (b) — Dependence of the flexural wave length in the rod on the distance to the free end in the frequency range from 10 to 100 kHz. The profile of the cut rod corresponding to the x coordinates of the graph is placed under the graph.

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8. Fig. 7. (a) — Sample rods, (b) — fastening of sample and transducers.

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9. Fig. 8. An example of visualization of the oscillation of the surface of a split rod obtained using a scanning vibrometer.

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10. Fig. 9. Amplitude-frequency characteristic of (a) control and (b) split rods in the range from 10 to 100 kHz.

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11. Fig. 10. Distribution of the amplitude of the bending mode (a) in the control sample and (b) in the split rod.

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12. Fig. 11. Dependence of the bending wave length in the rod on the distance to the free end in the frequency range from 10 to 100 kHz. The lines represent the simulation results, and the dots represent the experimental data.

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