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.
Similar content being viewed by others
References
Davis, H.: Biological and psychological effects of ultrasonics. J. Acoust. Soc. Am. 20, 605 (1948)
Dickson, E.D.D.: Some effects of intense sound and ultrasound on the ear. Proc. R. Soc. Med. 46, 139 (1952)
Smagowska, B.: Effects of ultrasonic noise on the human body-a bibliographic review. Int. J. Occup. Saf. Ergon. 19(2), 195 (2013)
Altmann, J.: Acoustic weapons—a prospective assessment. Sci. Global Secur. 9, 165 (2001)
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)
Rokhina, E.V., Lens, P., Virkutyte, J.: Low-frequency ultrasound in biotechnology: state of the art. Trends Biotechnol. 27(5), 298 (2009)
Nesterenko, V.F.: Dynamics of Heterogeneous Materials. Springer, New York (2001)
Sen, S., Hong, J., Bang, J., Avalos, E.: RobertDoney, solitary waves in the granular chain. Phys. Rep. 462, 21 (2008)
Tiwari, M., Mohan, T.R.K., Sen, S.: Impact decimation using alignment of granular spheres. Int. J. Mod. Phys. B 31, 1742012 (2017)
Rosas, A., Lindenberg, K.: Pulse propagation in granular chains: the binary collision approximation. Int. J. Mod. Phys. B 31, 1742016 (2017)
Gilcrist, L.E., Baker, G.S., Sen, S.: Preferred frequencies for three unconsolidated earth materials. Appl. Phys. Lett. 91, 254103 (2007)
Brunet, T., Jia, X., Mills, P.: Mechanisms for acoustic absorption in dry and weakly wet granular media. Phys. Rev. Lett. 101, 138001 (2008)
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)
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)
Lydon, J., Theocharis, G., Daraio, C.: Nonlinear resonances and energy transfer in finite granular chains. Phys. Rev. E 91, 023208 (2015)
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)
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)
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)
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)
Espíndola, D., Galaz, B., Melo, F.: Ultrasound induces aging in granular materials. Phys. Rev. Lett. 109, 158301 (2012)
Szelengowicz, I., Kevrekidis, P.G., Daraio, C.: Wave propagation in square granular crystals with spherical interstitial intruders. Phys. Rev. E 86, 061306 (2012)
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)
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)
Manciu, M., Sen, S., Hurd, A.J.: TImpulse propagation in dissipative and disordered chains with power-law repulsive potentials. Phys. D 157, 226 (2001)
Machado, L.P.S., Sen, S.: Controlled energy dispersion in 2D decorated granular crystals. Phys. Rev. E 98, 032907 (2018)
Machado, L.P.S., Rosas, A., Lindenberg, K.: Momentum and energy propagation in tapered granular chains. Granul. Matter 15, 735 (2013)
Machado, L.P.S., Rosas, A., Lindenberg, K.: A quasi-unidimensional granular chain to attenuate impact. Eur. Phys. J. E 37, 119 (2014)
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)
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.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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
Received:
Published:
DOI: https://doi.org/10.1007/s10035-019-0977-4