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Decorated granular crystal as filter of low-frequency ultrasonic signals

Abstract

We numerically study uncompressed granular crystals excited by sinusoidal signals at 1–100 kHz. A simple system such as two beads in a line reveals that for a fixed driven frequency, incident signals can be transmitted or filtered depending on the driving amplitude. We show that using square tapered crystals with decoration it becomes possible to enhance the low frequency filtration properties of granular systems. In addition to filtration, we find that \(80\%\) or more of the input force is attenuated using a crystal thickness of 4 grains.

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References

  1. Davis, H.: Biological and psychological effects of ultrasonics. J. Acoust. Soc. Am. 20, 605 (1948)

    ADS  Article  Google Scholar 

  2. Dickson, E.D.D.: Some effects of intense sound and ultrasound on the ear. Proc. R. Soc. Med. 46, 139 (1952)

    Google Scholar 

  3. Smagowska, B.: Effects of ultrasonic noise on the human body-a bibliographic review. Int. J. Occup. Saf. Ergon. 19(2), 195 (2013)

    Article  Google Scholar 

  4. Altmann, J.: Acoustic weapons—a prospective assessment. Sci. Global Secur. 9, 165 (2001)

    ADS  Article  Google Scholar 

  5. Feril Jr., L.B., Kondo, T.: Biological effects of low intensity ultrasound: the mechanism involved, and its implications on therapy and on biosafety of ultrasound. J. Radiat. Res. 45(4), 479 (2004)

    ADS  Article  Google Scholar 

  6. Rokhina, E.V., Lens, P., Virkutyte, J.: Low-frequency ultrasound in biotechnology: state of the art. Trends Biotechnol. 27(5), 298 (2009)

    Article  Google Scholar 

  7. Nesterenko, V.F.: Dynamics of Heterogeneous Materials. Springer, New York (2001)

    Book  Google Scholar 

  8. Sen, S., Hong, J., Bang, J., Avalos, E.: RobertDoney, solitary waves in the granular chain. Phys. Rep. 462, 21 (2008)

    ADS  MathSciNet  Article  Google Scholar 

  9. Tiwari, M., Mohan, T.R.K., Sen, S.: Impact decimation using alignment of granular spheres. Int. J. Mod. Phys. B 31, 1742012 (2017)

    ADS  Article  Google Scholar 

  10. Rosas, A., Lindenberg, K.: Pulse propagation in granular chains: the binary collision approximation. Int. J. Mod. Phys. B 31, 1742016 (2017)

    ADS  MathSciNet  Article  Google Scholar 

  11. Gilcrist, L.E., Baker, G.S., Sen, S.: Preferred frequencies for three unconsolidated earth materials. Appl. Phys. Lett. 91, 254103 (2007)

    ADS  Article  Google Scholar 

  12. Brunet, T., Jia, X., Mills, P.: Mechanisms for acoustic absorption in dry and weakly wet granular media. Phys. Rev. Lett. 101, 138001 (2008)

    ADS  Article  Google Scholar 

  13. Jayaprakash, K.R., Starosvetsky, Y., Vakakis, A.F., Peeters, M., Kerschen, G.: Nonlinear normal modes and band zones in granular chains with no pre-compression. Nonlinear Dyn. 63, 359 (2011)

    MathSciNet  Article  Google Scholar 

  14. Lydon, J., Jayaprakash, K.R., Ngo, D., Starosvetsky, Y., Vakakis, A.F., Daraio, C.: Frequency bands of strongly nonlinear homogeneous granular systems. Phys. Rev. E 88, 012206 (2013)

    ADS  Article  Google Scholar 

  15. Lydon, J., Theocharis, G., Daraio, C.: Nonlinear resonances and energy transfer in finite granular chains. Phys. Rev. E 91, 023208 (2015)

    ADS  Article  Google Scholar 

  16. Hutchins, D.A., Yang, J., Akanji, O., Thomas, P.J., Davies, L.A.J., Freear, S., Harput, S., Saffari, N., Gelat, P.: Evolution of ultrasonic impulses in chains of spheres using resonant excitation. Europhys. Lett. 109, 54002 (2015)

    ADS  Article  Google Scholar 

  17. Hutchins, D.A., Yang, J., Akanji, O., Thomas, P.J., Davis, L.A.J., Freear, S., Harput, S., Saffari, N., Gelat, P.: Ultrasonic propagation in finite-length granular chains. Ultrasonics 69, 215 (2016)

    Article  Google Scholar 

  18. Devaux, T., Tournat, V., Richoux, O., Pagneux, V.: Self-demodulation of elastic waves in a one-dimensional granular chain. Phys. Rev. E 70, 056603 (2004)

    Article  Google Scholar 

  19. Devaux, T., Tournat, V., Richoux, O., Pagneux, V.: Asymmetric acoustic propagation of wave packets via the self-demodulation effect. Phys. Rev. Lett. 115, 234301 (2015)

    ADS  Article  Google Scholar 

  20. Espíndola, D., Galaz, B., Melo, F.: Ultrasound induces aging in granular materials. Phys. Rev. Lett. 109, 158301 (2012)

    ADS  Article  Google Scholar 

  21. Szelengowicz, I., Kevrekidis, P.G., Daraio, C.: Wave propagation in square granular crystals with spherical interstitial intruders. Phys. Rev. E 86, 061306 (2012)

    ADS  Article  Google Scholar 

  22. Szelengowicz, I., Hasan, M.A., Starosvetsky, Y., Vakakis, A., Daraio, C.: Energy equipartition in two-dimensional granular systems with spherical intruders. Phys. Rev. E 87, 032204 (2013)

    ADS  Article  Google Scholar 

  23. Job, S., Santibanez, F., Tapia, F., Melo, F.: Wave localization in strongly nonlinear Hertzian chains with mass defect. Phys. Rev. E 80, 025602(R) (2009)

    ADS  Article  Google Scholar 

  24. Manciu, M., Sen, S., Hurd, A.J.: TImpulse propagation in dissipative and disordered chains with power-law repulsive potentials. Phys. D 157, 226 (2001)

    Article  Google Scholar 

  25. Machado, L.P.S., Sen, S.: Controlled energy dispersion in 2D decorated granular crystals. Phys. Rev. E 98, 032907 (2018)

    ADS  Article  Google Scholar 

  26. Machado, L.P.S., Rosas, A., Lindenberg, K.: Momentum and energy propagation in tapered granular chains. Granul. Matter 15, 735 (2013)

    Article  Google Scholar 

  27. Machado, L.P.S., Rosas, A., Lindenberg, K.: A quasi-unidimensional granular chain to attenuate impact. Eur. Phys. J. E 37, 119 (2014)

    Article  Google Scholar 

  28. Charalampidis, E., Li, F., Chong, C., Yang, J., Kevrekidis, P.G.: Time-periodic solutions of driven-damped trimer granular crystals. Math. Probl. Eng. 2015, 15 (2015)

    MathSciNet  Article  Google Scholar 

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Acknowledgements

The authors gratefully acknowledge financial support from the UFPA. L.M. also thanks the Department of Physics of UB for hospitality during his visit. S.S. was a recipient of a Fulbright-Nehru Academic and Professional Excellence Fellowship during the performance of this work.

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Correspondence to Luís Paulo Silveira Machado.

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Machado, L.P.S., Sen, S. Decorated granular crystal as filter of low-frequency ultrasonic signals. Granular Matter 22, 7 (2020). https://doi.org/10.1007/s10035-019-0977-4

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  • DOI: https://doi.org/10.1007/s10035-019-0977-4

Keywords

  • Ultrasonic signals
  • Filtration
  • Transmission
  • Granular filter
  • Decorated crystal