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Amplitude-activated mechanical wave manipulation devices using nonlinear metamaterials

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Abstract

We report device implications for acoustic metamaterials with various nonlinear oscillator microstructures as passive amplitude-activated mechanical wave filters and waveguides using simulations on their representative one-dimensional discrete element models. Linear and various nonlinear hardening and softening stiffness cases and combinations thereof are considered for the local oscillators. The propagation and attenuation characteristics of harmonic waves in a tunable frequency range are found to correspond to the excitation amplitude and nonlinearity-dependent shifts in the local resonance bandgap for such nonlinear acoustic metamaterials. Three passive acoustic devices—(i) amplitude-activated selective filter, (ii) amplitude band pass or band rejection filter, and (iii) direction-biased waveguide—are demonstrated numerically. Constituent frequency components in bifrequency excitations are shown to be retained or diminished to varying degrees within acoustic metamaterials with either hardening or softening local oscillators depending on their individual amplitudes. Using trilinear hardening or softening oscillators instead switches the response between attenuation and propagation respectively, outside of a tunable bandwidth of amplitude for the same excitation frequency. Whereas, amplitude-dependent, passive direction-bias in propagation characteristics for a given excitation frequency is demonstrated in a metamaterial waveguide composed of units with tuned combinations of linear and nonlinear hardening oscillators deployed in sequence. These predictions indicate the possibility of realizing acoustic metamaterials having passive adaptive, amplitude-activated dynamics using tailored combinations of nonlinear oscillators to elicit prescribed wave transformations across them.

Passive adaptive devices for amplitude-selective filtering, band passage or rejection, and direction-biased propagation using nonlinear acoustic metamaterials is demonstrated numerically. Fig. A (a) Transmissibility versus excitation amplitude for trilinear hardening (TLH) and softening (TLS) cases; (b) Input and output spectra for left to right and right to left propagation in the direction-biased waveguide.

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References

  1. Martinez-Sala R, Sancho J, Sanchez JV, Gomez V, Llinares J, Meseguer F (1995) Sound attenuation by sculpture. Nature 378:241–241

    Article  CAS  Google Scholar 

  2. Sánchez-Pérez JV, Caballero D, Mártinez-Sala R, Rubio C, Sánchez-Dehesa J, Meseguer F et al (1998) Sound attenuation by a two-dimensional array of rigid cylinders. Phys Rev Lett 80:5325–5328

    Article  Google Scholar 

  3. Vincent JH (1898) LX. On the construction of a mechanical model to illustrate Helmholtz’s theory of dispersion. Philos Maga 46:557–563

    Article  Google Scholar 

  4. Liu Z, Zhang X, Mao Y, Zhu YY, Yang Z, Chan CT et al (2000) Locally resonant sonic materials. Science 289:1734–1736

    Article  CAS  Google Scholar 

  5. Huang HH, Sun CT, Huang GL (2009) On the negative effective mass density in acoustic metamaterials. Int J Eng Sci 47:610–617

    Article  CAS  Google Scholar 

  6. Popa BI, Zigoneanu L, Cummer SA (2011) Experimental acoustic ground cloak in air. Phys Rev Lett 106:253901

    Article  Google Scholar 

  7. Ambati M, Fang N, Sun C, Zhang X (2007) Surface resonant states superlensing in acoustic metamaterials. Phys Rev B 75:195447

    Article  Google Scholar 

  8. Zhang S, Yin L, Fang N (2009) Focusing ultrasound with an acoustic metamaterial network. Phys Rev Lett 102:194301

    Article  Google Scholar 

  9. Yang Z, Mei J, Yang M, Chan NH, Sheng P (2008) Membrane-type acoustic metamaterial with negative dynamic mass. Phys Rev Lett 101:204301

    Article  CAS  Google Scholar 

  10. Chen Y, Liu H, Reilly M, Bae H, Yu M (2014) Enhanced acoustic sensing through wave compression pressure amplification in anisotropic metamaterials. Nat Commun 5:5247

    Article  CAS  Google Scholar 

  11. Kulkarni PP, Manimala JM (2016) Longitudinal elastic wave propagation characteristics of inertant acoustic metamaterials. Jpn J Appl Phys 119:245101

    Article  Google Scholar 

  12. Wang G, Wen X, Wen J, Shao L, Liu Y (2004) Two-dimensional locally resonant phononic crystals with binary structures. Phys Rev Lett 93:154302

    Article  Google Scholar 

  13. Lazarov BS, Jensen JS (2007) Low-frequency b gaps in chains with attached non-linear oscillators. Int J Nonlin Mech 42:1186–1193

    Article  Google Scholar 

  14. Manimala JM, Sun CT (2016) Numerical investigation of amplitude-dependent dynamic response in acoustic metamaterials with nonlinear oscillators. J Acoust Soc Am 139:3365–3372

    Article  Google Scholar 

  15. Kulkarni PP, Manimala JM (2018) Nonlinear Inertant Acoustic Metamaterials their Device Implications, in proceedings of the SEM Annual Conference on Experimental Mechanics, Indiana, USA

  16. Xiao Y, Wen J, Wang G, Wen X (2013) Theoretical experimental study of locally resonant Bragg band gaps in flexural beams carrying periodic arrays of beam-like resonators. J Vib Acoust 135:041006–041006

    Article  Google Scholar 

  17. Lee SH, Park CM, Seo YM, Wang ZG, Kim CK (2009) Acoustic metamaterial with negative density. Phys Lett A 373:4464–4469

    Article  CAS  Google Scholar 

  18. Lee SH, Park CM, Seo YM, Wang ZG, Kim CK (2010) Composite acoustic medium with simultaneously negative density modulus. Phys Rev Lett 104:054301

    Article  Google Scholar 

  19. Boechler N, Theocharis G, Daraio C (2011) Bifurcation-based acoustic switching rectification. Nat Mater 10:665–668

    Article  CAS  Google Scholar 

  20. Zhang H, Xiao Y, Wen J, Yu D, Wen X (2016) Ultra-thin smart acoustic metasurface for low-frequency sound insulation. Appl Phys Lett 108:141902

    Article  Google Scholar 

  21. Manimala JM, Huang HH, Sun CT, Snyder R, Bl S (2014) Dynamic load mitigation using negative effective mass structures. Eng Struct 80:458–468

    Article  Google Scholar 

  22. Smith TL, Rao K, Dyer I (1986) Attenuation of plate flexural waves by a layer of dynamic absorbers. The National Academies of Sciences, Engineering, Medicine

  23. Nadkarni N, Arrieta AF, Chong C, Kochmann DM, Daraio C (2016) Unidirectional transition waves in bistable lattices. Phys Rev Lett 116:244501

    Article  Google Scholar 

  24. Zhai S, Chen H, Ding C, Shen F, Luo C, Zhao X (2015) Manipulation of transmitted wave front using ultrathin planar acoustic metasurfaces. Appl Phys A - Mater 120:1283–1289

    Article  CAS  Google Scholar 

  25. Zhu R, Chen Y, Barnhart M, Hu G, Sun C, Huang G (2016) Experimental study of an adaptive elastic metamaterial controlled by electric circuits. Appl Phys Lett 108:011905

    Article  Google Scholar 

  26. Popa BI, Cummer SA (2014) Non-reciprocal highly nonlinear active acoustic metamaterials. Nat Commun 5:3398

    Article  Google Scholar 

  27. Xiao S, Ma G, Li Y, Yang Z, Sheng P (2015) Active control of membrane-type acoustic metamaterial by electric field. Appl Phys Lett 106:091904

    Article  Google Scholar 

  28. Maznev AA, Every AG, Wright OB (2013) Reciprocity in reflection transmission: what is a ‘phonon diode’? Wave Motion 50:776–784

    Article  Google Scholar 

  29. Narisetti RK, Leamy MJ, Ruzzene M (2010) A perturbation approach for predicting wavepropagation in one-dimensional nonlinear periodic structures. J Vib Acoust 132:031001

    Article  Google Scholar 

  30. Casalotti A, El-Borgi S, Lacarbonara W (2018) Metamaterial beam with embedded nonlinear vibration absorbers. Int J Nonlin Mech 98:32–42

    Article  Google Scholar 

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Funding

J. M. and K. M. received support through Defense Advanced Research Projects Agency (DARPA) Grant No. D16AP00032 during the completion of this work.

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Authors and Affiliations

  1. School of Mechanical & Aerospace Engineering, Oklahoma State University, 218, Engineering North, Stillwater, OK, 74078, USA

    James M. Manimala, Prateek P. Kulkarni & Karthik Madhamshetty

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  1. James M. Manimala
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  2. Prateek P. Kulkarni
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  3. Karthik Madhamshetty
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Correspondence to James M. Manimala.

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Manimala, J.M., Kulkarni, P.P. & Madhamshetty, K. Amplitude-activated mechanical wave manipulation devices using nonlinear metamaterials. Adv Compos Hybrid Mater 1, 797–808 (2018). https://doi.org/10.1007/s42114-018-0068-8

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  • DOI: https://doi.org/10.1007/s42114-018-0068-8

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