- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Applied

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Nonreciprocal Wave Propagation in a Continuum-Based Metamaterial with Space-Time Modulated Resonators

Yangyang Chen1, Xiaopeng Li1, Hussein Nassar1, Andrew N. Norris2, Chiara Daraio3, and Guoliang Huang1,*

  • 1Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri 65211, USA
  • 2Mechanical and Aerospace Engineering, Rutgers University, Piscataway, New Jersey 08854, USA
  • 3Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA

  • *huangg@missouri.edu
PDF

Phys. Rev. Applied 11, 064052 – Published 21 June, 2019

DOI: https://doi.org/10.1103/PhysRevApplied.11.064052

Abstract

Breaking reciprocity with spatiotemporal modulation provides an opportunity to design unprecedented optical, acoustic, and mechanical waveguides. A main challenge is to physically realize continuum-based metamaterials whose properties can be rapidly tuned in both space and time at the length and time scales of the propagated waves. We design a tunable elastic metamaterial by embedding in a beam a set of permanent magnets, and placing oscillating electrical coils coaxially adjacent to each magnet. By programming in space and time the ac input of the coils, the magnet-coil effective coupling stiffness is modulated along with the resonance frequency. Distinctly nonreciprocal flexural wave propagation is then experimentally observed. In addition, robust tunability of unidirectional band gaps and wave energy bias are quantitatively analyzed by applying different modulation current amplitudes, material damping coefficients, and modulation frequencies. Both simplified analytical and finite-element-method-based numerical models of the modulated metamaterial are suggested and analyzed in support of the experimental work. Specifically, unidirectional frequency conversions and band gaps due to the second-order mode interactions are discussed for the first time when the large modulation amplitude is implemented. The suggested prototype sheds light on nonreciprocal waveguiding, which could be applied in advanced wave diodes, phononic logic, energy localization, trapping, and harvesting.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (36)

  1. J. D. Achenbach, Reciprocity in Elastodynamics (Cambridge University Press, Cambridge, UK, 2003).
  2. H. Lamb, On reciprocal theorems in dynamics, Proc. Lond. Math. Soc. 19, 144 (1888).
  3. R. Fleury, D. L. Sounas, M. R. Haberman, and A. Alù, Nonreciprocal acoustics, Acoust. Today 11, 14 (2015).
  4. S. A. Cummer, J. Christensen, and A. Alù, Controlling sound with acoustic metamaterials, Nat. Rev. Mater. 1, 16001 (2016).
  5. R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, Sound isolation and giant linear nonreciprocity in a compact acoustic circulator, Science 343, 516 (2014).
  6. B. Liang, X. S. Guo, J. Tu, D. Zhang, and J. C. Cheng, An acoustic rectifier, Nat. Mater. 9, 989 (2010).
  7. G. Trainiti and M. Ruzzene, Non-reciprocal elastic wave propagation in spatiotemporal periodic structures, New J. Phys. 18, 083047 (2016).
  8. K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, Breaking Lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering, Science 356, 1260 (2017).
  9. X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, Tunable Unidirectional Sound Propagation Through a Sonic-Crystal-Based Acoustic Diode, Phys. Rev. Lett. 106, 084301 (2011).
  10. N. Boechler, G. Theocharis, and C. Daraio, Bifurcation-based acoustic switching and rectification, Nat. Mater. 10, 665 (2011).
  11. P. Wang, L. Lu, and K. Bertoldi, Topological Phononic Crystals with One-Way Elastic Edge Waves, Phys. Rev. Lett. 115, 104302 (2015).
  12. L. M. Nash, D. Kleckner, A. Read, V. Vitelli, A. M. Turner, and W. T. M. Irvine, Topological mechanics of gyroscopic metamaterials, Proc. Natl. Acad. Sci. 112, 14495 (2015).
  13. Z. Zhang, I. Koroleva, L. I. Manevitch, L. A. Bergman, and A. F. Vakakis, Nonreciprocal acoustics and dynamics in the in-plane oscillations of a geometrically nonlinear lattice, Phys. Rev. E 94, 032214 (2016).
  14. D. L. Sounas and A. Alù, Non-reciprocal photonics based on time modulation, Nat. Photonics 11, 774 (2017).
  15. E. Cassedy and A. Oliner, Dispersion relations in time-space periodic media: Part I-stable interactions, Proc. IEEE 51, 1342 (1963).
  16. E. Cassedy, Dispersion relations in time-space periodic media: Part II-Unstable interactions, Proc. IEEE 55, 1154 (1967).
  17. N. Swinteck, S. Matsuo, K. Runge, J. O. Vasseur, P. Lucas, and P. A. Deymier, Bulk elastic waves with unidirectional backscattering-immune topological states in a time-dependent superlattice, J. Appl. Phys. 118, 063103 (2015).
  18. H. Nassar, H. Chen, A. N. Norris, M. R. Haberman, and G. L. Huang, Non-reciprocal wave propagation in modulated elastic metamaterials, Proc. R. Soc. A 473, 20170188 (2017).
  19. H. Nassar, H. Chen, A. Norris, and G. Huang, Non-reciprocal flexural wave propagation in a modulated metabeam, Extreme Mech. Lett. 15, 97 (2017).
  20. M. H. Ansari, M. A. Attarzadeh, M. Nouh, and M. A. Karami, Application of magnetoelastic materials in spatiotemporally modulated phononic crystals for nonreciprocal wave propagation, Smart Mater. Struct. 27, 015030 (2017).
  21. K. Yi, M. Collet, and S. Karkar, Frequency conversion induced by time-space modulated media, Phys. Rev. B 96, 104110 (2017).
  22. H. Nassar, X. Xu, A. Norris, and G. Huang, Modulated phononic crystals: Non-reciprocal wave propagation and Willis materials, J. Mech. Phys. Solids 101, 10 (2017).
  23. S. P. Wallen and M. R. Haberman, Non-reciprocal wave phenomena in spring-mass chains with effective stiffness modulation induced by geometric nonlinearity, Phys. Rev. E 99, 013001 (2019).
  24. Y. Wang, B. Yousefzadeh, H. Chen, H. Nassar, G. Huang, and C. Daraio, Observation of Nonreciprocal Wave Propagation in a Dynamic Phononic Lattice, Phys. Rev. Lett. 121, 194301 (2018).
  25. J. Gump, I. Finkler, H. Xia, R. Sooryakumar, W. J. Bresser, and P. Boolchand, Light-Induced Giant Softening of Network Glasses Observed Near the Mean-Field Rigidity Transition, Phys. Rev. Lett. 92, 245501 (2004).
  26. N. Swinteck, S. Matsuo, K. Runge, J. O. Vasseur, P. Lucas, and P. A. Deymier, Photoplastic effects in chalcogenide glasses: A review, Phys. Status Solids B 246, 1773 (2009).
  27. F. Casadei, T. Delpero, A. Bergamini, P. Ermanni, and M. Ruzzene, Piezoelectric resonator arrays for tunable acoustic waveguides and metamaterials, J. Appl. Phys. 112, 064902 (2012).
  28. Y. Y. Chen, G. L. Huang, and C. T. Sun, Band gap control in an active elastic metamaterial with negative capacitance piezoelectric shunting, J. Vib. Acoust. 136, 061008 (2014).
  29. Y. Y. Chen, R. Zhu, M. V. Barnhart, and G. L. Huang, Enhanced flexural wave sensing by adaptive gradient-index metamaterials, Sci. Rep. 6, 35048 (2016).
  30. G. Wang, J. Cheng, J. Chen, and Y. He, Multi-resonant piezoelectric shunting induced by digital controllers for subwavelength elastic wave attenuation in smart metamaterial, Smart Mater. Struct. 26, 025031 (2017).
  31. Y. Y. Chen, G. K. Hu, and G. L. Huang, An adaptive metamaterial beam with hybrid shunting circuits for extremely broadband control of flexural waves, Smart Mater. Struct. 25, 105036 (2016).
  32. Y. Y. Chen, G. K. Hu, and G. L. Huang, A hybrid elastic metamaterial with negative mass density and tunable bending stiffness, J. Mech. Phys. Solids 105, 179 (2017).
  33. X. P. Li, Y. Y. Chen, G. K. Hu, and G. L. Huang, A self-adaptive metamaterial beam with digitally controlled resonators for subwavelength broadband flexural wave attenuation, Smart Mater. Struct. 27, 045015 (2018).
  34. K. Danas, S. V. Kankanala, and N. Triantafyllidis, Experiments and modeling of iron-particle-filled magnetorheological elastomers, J. Mech. Phys. Solids 60, 120 (2012).
  35. E. J. Reed, M. Soljačić, and J. D. Joannopoulos, Reversed Doppler Effect in Photonic Crystals, Phys. Rev. Lett. 91, 133901 (2003).
  36. M. Vachon, Dynamic response of 3D printed beams with damping layers (Massachusetts Institute of Technology, Thesis, 2015).

Outline

Information

Phys. Rev. Applied 11, 064052– Published 21 June, 2019
  • Received 14 March 2019
  • Revised 20 May 2019
Article part of CHORUS
Crossmark - Check for updates button

© 2019 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation