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Realizing passive direction-bias for mechanical wave propagation using a nonlinear metamaterial

  • Prateek P. Kulkarni
  • James M. ManimalaEmail author
Original Paper
  • 7 Downloads

Abstract

The possibility of realizing amplitude-activated passive direction-bias in longitudinal elastic wave propagation using a nonlinear acoustic metamaterial is demonstrated. Applying the method of multiple scales, approximate analytical solutions are derived for the dispersion curve and bandgap shifts due to the presence of nonlinear hardening local oscillators within the metamaterial using its lumped parameter effective-mass model. The configuration for a structural waveguide consisting of a tuned combination of a nonlinear and a linear acoustic metamaterial that takes advantage of these shifts to produce amplitude-activated direction-bias in propagation was postulated and verified using discrete element simulations. A numerical routine to generate root profile geometries that enable contact-based hardening response in tip-loaded cantilever beam resonators was developed and implemented. Utilizing a hybrid fabrication process involving additively manufactured and machined components, a prototype test article was constructed. Experiments using a structural waveguide test rig verify the existence and extent of bandgaps and provide evidence for the passive direction-bias phenomenon. Follow-on investigations on configurations with different types of nonlinearities could pave the way for development of additional passive acoustic wave manipulation devices with enriched dynamics.

Notes

Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.

References

  1. 1.
    Pendry, J.B.: Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000)CrossRefGoogle Scholar
  2. 2.
    Shelby, R.A., Smith, D.R., Schultz, S.: Experimental verification of a negative index of refraction. Science 292, 77–79 (2001)CrossRefGoogle Scholar
  3. 3.
    Liu, Z., Zhang, X., Mao, Y., Zhu, Y.Y., Yang, Z., Chan, C.T., et al.: Locally resonant sonic materials. Science 289, 1734–1736 (2000)CrossRefGoogle Scholar
  4. 4.
    Huang, H.H., Sun, C.T., Huang, G.L.: On the negative effective mass density in acoustic metamaterials. Int. J. Eng. Sci. 47, 610–617 (2009)CrossRefGoogle Scholar
  5. 5.
    Sukhovich, A., Merheb, B., Muralidharan, K., Vasseur, J.O., Pennec, Y., Deymier, P.A., et al.: Experimental and theoretical evidence for subwavelength imaging in phononic crystals. Phys. Rev. Lett. 102, 154301 (2009)CrossRefGoogle Scholar
  6. 6.
    Sanchis, L., García-Chocano, V.M., Llopis-Pontiveros, R., Climente, A., Martínez-Pastor, J., Cervera, F., et al.: Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere. Phys. Rev. Lett. 110, 124301 (2013)CrossRefGoogle Scholar
  7. 7.
    Romero-García, V., Theocharis, G., Richoux, O., Merkel, A., Tournat, V., Pagneux, V.: Perfect and broadband acoustic absorption by critically coupled sub-wavelength resonators. Sci. Rep. 6, 19519 (2016)CrossRefGoogle Scholar
  8. 8.
    Ma, G., Yang, M., Xiao, S., Yang, Z., Sheng, P.: Acoustic metasurface with hybrid resonances. Nat. Mater. 13, 873–878 (2014)CrossRefGoogle Scholar
  9. 9.
    Viktor, G.V.: The electrodynamics of substances with simultaneously negative values of \(\varepsilon \) and \(\mu \). Phys. Uspekhi 10, 509 (1968)CrossRefGoogle Scholar
  10. 10.
    Lakes, R.S., Lee, T., Bersie, A., Wang, Y.C.: Extreme damping in composite materials with negative-stiffness inclusions. Nature 410, 565–567 (2001)CrossRefGoogle Scholar
  11. 11.
    Manimala, J.M., Huang, H.H., Sun, C.T., Snyder, R., Bland, S.: Dynamic load mitigation using negative effective mass structures. Eng. Struct. 80, 458–468 (2014)CrossRefGoogle Scholar
  12. 12.
    Milton, G.W., Willis, J.R.: On modifications of Newton’s second law and linear continuum elastodynamics. Proc. R. Soc. Lond. A 463, 855–880 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Huang, H.H., Sun, C.T.: Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and Young’s modulus. J. Acoust. Soc. Am. 132, 2887–2895 (2012)CrossRefGoogle Scholar
  14. 14.
    Huang, H.H., Sun, C.T.: Theoretical investigation of the behavior of an acoustic metamaterial with extreme Young’s modulus. J. Mech. Phys. Solids 59, 2070–2081 (2011)CrossRefzbMATHGoogle Scholar
  15. 15.
    Vincent, J.H.: LX. On the construction of a mechanical model to illustrate Helmholtz’s theory of dispersion. Philos. Mag. 46, 557–563 (1898)CrossRefzbMATHGoogle Scholar
  16. 16.
    Fang, N., Xi, D., Xu, J., Ambati, M., Srituravanich, W., Sun, C., et al.: Ultrasonic metamaterials with negative modulus. Nat. Mater. 5, 452–456 (2006)CrossRefGoogle Scholar
  17. 17.
    Lee, S.H., Park, C.M., Seo, Y.M., Wang, Z.G., Kim, C.K.: Acoustic metamaterial with negative density. Phys. Lett. A 373, 4464–4469 (2009)CrossRefGoogle Scholar
  18. 18.
    Lee, S.H., Park, C.M., Seo, Y.M., Wang, Z.G., Kim, C.K.: Composite acoustic medium with simultaneously negative density and modulus. Phys. Rev. Lett. 104, 054301 (2010)CrossRefGoogle Scholar
  19. 19.
    Liu, Z., Chan, C.T., Sheng, P., Goertzen, A.L., Page, J.H.: Elastic wave scattering by periodic structures of spherical objects: theory and experiment. Phys. Rev. B 62, 2446–2457 (2000)CrossRefGoogle Scholar
  20. 20.
    Sheng, P., Zhang, X.X., Liu, Z., Chan, C.T.: Locally resonant sonic materials. Physica B 338, 201–205 (2003)CrossRefGoogle Scholar
  21. 21.
    Manimala, J.M., Sun, C.T.: Microstructural design studies for locally dissipative acoustic metamaterials. J. Appl. Phys. 115, 023518 (2014)CrossRefGoogle Scholar
  22. 22.
    Baravelli, E., Carrara, M., Ruzzene, M.: High stiffness, high damping chiral metamaterial assemblies for low-frequency applications. In: Health Monitoring of Structural and Biological Systems, San Dieo, USA, pp. 86952K–86952K-10 (2013)Google Scholar
  23. 23.
    Li, J., Chan, C.T.: Double-negative acoustic metamaterial. Phys. Rev. E 70, 055602 (2004)CrossRefGoogle Scholar
  24. 24.
    Hirsekorn, M.: Small-size sonic crystals with strong attenuation bands in the audible frequency range. Appl. Phys. Lett. 84, 3364–3366 (2004)CrossRefGoogle Scholar
  25. 25.
    Huang, H.H., Sun, C.T.: Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density. N. J. Phys. 11, 013003 (2009)CrossRefGoogle Scholar
  26. 26.
    Cveticanin, L., Zukovic, M.: Negative effective mass in acoustic metamaterial with nonlinear mass-in-mass subsystems. Commun. Nonlinear Sci. Numer. Simul. 51, 89–104 (2017)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Narisetti, R.K., Leamy, M.J., Ruzzene, M.: A perturbation approach for predicting wave propagation in one-dimensional nonlinear periodic structures. J. Vib. Acoust. 132, 031001 (2010)CrossRefGoogle Scholar
  28. 28.
    Liu, X., Huang, X., Hua, H.: On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. J. Sound Vib. 332, 3359–3376 (2013)CrossRefGoogle Scholar
  29. 29.
    Rudenko, O.V.: Giant nonlinearities in structurally inhomogeneous media and the fundamentals of nonlinear acoustic diagnostic techniques. Physics-Uspekhi 49, 69–87 (2006)CrossRefGoogle Scholar
  30. 30.
    Guo, X., Lin, Z., Tu, J., Liang, B., Cheng, J., Zhang, D.: Modeling and optimization of an acoustic diode based on micro-bubble nonlinearity. J. Acoust. Soc. Am. 133, 1119–1125 (2013)CrossRefGoogle Scholar
  31. 31.
    Popa, B.-I., Cummer, S.A.: Non-reciprocal and highly nonlinear active acoustic metamaterials. Nat. Commun. 5, 3398 (2014)CrossRefGoogle Scholar
  32. 32.
    Wang, Y.-Z., Wang, Y.-S.: Active control of elastic wave propagation in nonlinear phononic crystals consisting of diatomic lattice chain. Wave Motion 78, 1–8 (2018)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Nadkarni, N., Arrieta, A.F., Chong, C., Kochmann, D.M., Daraio, C.: Unidirectional transition waves in bistable lattices. Phys. Rev. Lett. 116, 244501 (2016)CrossRefGoogle Scholar
  34. 34.
    Mann, B.P., Sims, N.D.: Energy harvesting from the nonlinear oscillations of magnetic levitation. J. Sound Vib. 319, 515–530 (2009)CrossRefGoogle Scholar
  35. 35.
    Jutte, C.V., Kota, S.: Design of nonlinear springs for prescribed load-displacement functions. J. Mech. Des. 130, 081403–081403 (2008)CrossRefGoogle Scholar
  36. 36.
    Oh, J.H., Kim, H.W., Ma, P.S., Seung, H.M., Kim, Y.Y.: Inverted bi-prism phononic crystals for one-sided elastic wave transmission applications. Appl. Phys. Lett. 100, 213503 (2012)CrossRefGoogle Scholar
  37. 37.
    Liang, B., Yuan, B., Cheng, J.-C.: Acoustic diode: rectification of acoustic energy flux in one-dimensional systems. Phys. Rev. Lett. 103, 104301 (2009)CrossRefGoogle Scholar
  38. 38.
    Liang, B., Guo, X.S., Tu, J., Zhang, D., Cheng, J.C.: An acoustic rectifier. Nat. Mater. 9, 989 (2010)CrossRefGoogle Scholar
  39. 39.
    Sun, H.-X., Zhang, S.-Y., Shui, X.-J.: A tunable acoustic diode made by a metal plate with periodical structure. Appl. Phys. Lett. 100, 103507 (2012)CrossRefGoogle Scholar
  40. 40.
    Gu, Z.-M., Hu, J., Liang, B., Zou, X.-Y., Cheng, J.-C.: Broadband non-reciprocal transmission of sound with invariant frequency. Nat. Sci. Rep. 6, 19824 (2016)CrossRefGoogle Scholar
  41. 41.
    Jiang, X., Liang, B., Zou, X.-Y., Yang, J., Yin, L.-L., Yang, J., Cheng, J.-C.: Acoustic one-way metasurfaces: asymmetric phase modulation of sound by subwavelength layer. Nat. Sci. Rep. 6, 28023 (2016)CrossRefGoogle Scholar
  42. 42.
    Manimala, J.M., Kulkarni, P.P., Madhamshetty, K.: Amplitude-activated mechanical wave manipulation devices using nonlinear metamaterials. Adv. Compos. Hybrid Mater. 1(4), 797–808 (2018)CrossRefGoogle Scholar
  43. 43.
    Spreemann, D., Folkmer, B., Manoli, Y.: Realization of nonlinear hardening springs with predefined characteristic for vibration transducers based on beam structures. MikroSystemTechnik (2011)Google Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical and Aerospace EngineeringOklahoma State UniversityStillwaterUSA

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