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

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Scattering of waves in locally resonant woodpile structures with impurities

Yeongtae Jang1,2, Eunho Kim3,4,5,*, and Junsuk Rho1,6,7,8,†

  • *Contact author: eunhokim@jbnu.ac.kr
  • †Contact author: jrsho@postech.ac.kr
PDF

Phys. Rev. E 114, 035503 – Published 4 September, 2026

DOI: https://doi.org/10.1103/rwtw-8tvm

Abstract

We theoretically and experimentally investigate wave scattering in a single-column woodpile structure with impurities. This structure consists of slender cylindrical beams that support flexural bending modes, which are coupled strongly with propagating waves in the low-frequency regime (i.e., local resonance coupling). We examine the linear scattering of plane waves from single and double impurities in periodic configurations. When local resonance coupling is neglected, the double-impurity configuration exhibits reflectionless transmission, resembling the Ramsauer-Townsend (RT) resonance. Further analysis reveals that, under strong local resonance coupling, this behavior evolves into a Fano resonance, which features an asymmetric line shape with a sharp transition between transmission and reflection. However, as the RT resonance and the local resonance become spectrally closer, an analog of electromagnetically induced transparency (EIT) emerges, resulting from the balanced interference between the two modes. These distinct resonant behaviors can be tuned by varying the local resonance coupling strength, providing a controllable platform for macroscopic analogs of quantum wave interference. Potential applications include vibration isolation and wave-based switching devices.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (46)

  1. V. F. Nesterenko, Dynamics of Heterogeneous Materials (Springer, New York, NY, 2001).
  2. M. A. Porter, P. G. Kevrekidis, and C. Daraio, Granular crystals: Nonlinear dynamics meets materials engineering, Phys. Today 68(11), 44 (2015).
  3. C. Chong, M. A. Porter, P. G. Kevrekidis, and C. Daraio, Nonlinear coherent structures in granular crystals, J. Phys.: Condens. Matter 29, 413003 (2017).
  4. S. Sen, J. Hong, J. Bang, E. Avalos, and R. Doney, Solitary waves in the granular chain, Phys. Rep. 462, 21 (2008).
  5. P. G. Kevrekidis, Non-linear waves in lattices: Past, present, future, IMA J. Appl. Math. 76, 389 (2011).
  6. G. Theocharis, N. Boechler, and C. Daraio, Nonlinear periodic phononic structures and granular crystals, in Acoustic Metamaterials and Phononic Crystals (Springer, Berlin, Heidelberg, 2012), pp. 217–251.
  7. M. Meidani, E. Kim, F. Li, J. Yang, and D. Ngo, Tunable evolutions of wave modes and bandgaps in quasi-1D cylindrical phononic crystals, J. Sound Vib. 334, 270 (2015).
  8. R. Chaunsali, E. Kim, A. Thakkar, P. Kevrekidis, and J. Yang, Demonstrating an in situ topological band transition in cylindrical granular chains, Phys. Rev. Lett. 119, 024301 (2017).
  9. J. Hong, Universal power-law decay of the impulse energy in granular protectors, Phys. Rev. Lett. 94, 108001 (2005).
  10. R. Chaunsali, M. Toles, J. Yang, and E. Kim, Extreme control of impulse transmission by cylinder-based nonlinear phononic crystals, J. Mech. Phys. Solids 107, 21 (2017).
  11. Y. Jang, E. Kim, J. Yang, and J. Rho, Sculpt wave propagation in 3D woodpile architecture through vibrational mode coupling, Mech. Syst. Sig. Process. 224, 112112 (2025).
  12. N. Boechler, G. Theocharis, and C. Daraio, Bifurcation-based acoustic switching and rectification, Nat. Mater. 10, 665 (2011).
  13. E. Kim, R. Chaunsali, and J. Yang, Gradient-index granular crystals: From boomerang motion to asymmetric transmission of waves, Phys. Rev. Lett. 123, 214301 (2019).
  14. F. Li, P. Anzel, J. Yang, P. G. Kevrekidis, and C. Daraio, Granular acoustic switches and logic elements, Nat. Commun. 5, 5311 (2014).
  15. J. Yang, C. Silvestro, S. N. Sangiorgio, S. L. Borkowski, E. Ebramzadeh, L. D. Nardo, and C. Daraio, Nondestructive evaluation of orthopaedic implant stability in THA using highly nonlinear solitary waves, Smart Mater. Struct. 21, 012002 (2012).
  16. E. Kim and J. Yang, Wave propagation in single column woodpile phononic crystals: Formation of tunable band gaps, J. Mech. Phys. Solids 71, 33 (2014).
  17. E. Kim, F. Li, C. Chong, G. Theocharis, J. Yang, and P. Kevrekidis, Highly nonlinear wave propagation in elastic woodpile periodic structures, Phys. Rev. Lett. 114, 118002 (2015).
  18. E. Kim, J. Yang, H. Hwang, and C. W. Shul, Impact and blast mitigation using locally resonant woodpile metamaterials, Int. J. Impact Eng. 101, 24 (2017).
  19. Y. Jang, B. Oh, E. Kim, and J. Rho, Bidirectional asymmetric frequency conversion in nonlinear phononic crystals, Phys. Rev. Lett. 135, 036603 (2025).
  20. Y. Jang, S. Kim, M. Kim, G. Kim, E. Kim, and J. Rho, Mode-coupled infinite topological edge state in bulk-lattice-merged mechanical Su-Schrieffer-Heeger chain, Extreme Mech. Lett. 77, 102334 (2025).
  21. Y. Jang, S. Kim, E. Kim, and J. Rho, Singular topological edge states in locally resonant metamaterials, Sci. Bull. 70, 1080 (2025).
  22. Y. Jang, S. Kim, D. Lee, E. Kim, and J. Rho, Bound states to bands in the continuum in cylindrical granular crystals, Phys. Rev. Lett. 134, 136901 (2025).
  23. Y. Jang, E. Kim, J. Yang, and J. Rho, Physics-informed discrete element modeling for the bandgap engineering of cylinder chains, Appl. Math. Modell. 125, 571 (2024).
  24. A. J. Martínez, H. Yasuda, E. Kim, P. G. Kevrekidis, M. A. Porter, and J. Yang, Scattering of waves by impurities in precompressed granular chains, Phys. Rev. E 93, 052224 (2016).
  25. J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics (Cambridge University Press, Cambridge, UK, 2020).
  26. L. Novotny, Strong coupling, energy splitting, and level crossings: A classical perspective, Am. J. Phys. 78, 1199 (2010).
  27. C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussenzveig, Classical analog of electromagnetically induced transparency, Am. J. Phys. 70, 37 (2002).
  28. W. Frank and P. von Brentano, Classical analogy to quantum mechanical level repulsion, Am. J. Phys. 62, 706 (1994).
  29. H. J. Maris and Q. Xiong, Adiabatic and nonadiabatic processes in classical and quantum mechanics, Am. J. Phys. 56, 1114 (1988).
  30. M. Hasan, Y. Starosvetsky, A. Vakakis, and L. Manevitch, Nonlinear targeted energy transfer and macroscopic analog of the quantum Landau-Zener effect in coupled granular chains, Physica D 252, 46 (2013).
  31. C. Wang, A. Kanj, A. Mojahed, S. Tawfick, and A. F. Vakakis, Experimental Landau-Zener tunneling for wave redirection in nonlinear waveguides, Phys. Rev. Appl. 14, 034053 (2020).
  32. A. J. Martínez, P. G. Kevrekidis, and M. A. Porter, Superdiffusive transport and energy localization in disordered granular crystals, Phys. Rev. E 93, 022902 (2016).
  33. E. Kim, A. J. Martínez, S. E. Phenisee, P. G. Kevrekidis, M. A. Porter, and J. Yang, Direct measurement of superdiffusive energy transport in disordered granular chains, Nat. Commun. 9, 640 (2018).
  34. S. D. Huber, Topological mechanics, Nat. Phys. 12, 621 (2016).
  35. H. Nassar, B. Yousefzadeh, R. Fleury, M. Ruzzene, A. Alù, C. Daraio, A. N. Norris, G. Huang, and M. R. Haberman, Nonreciprocity in acoustic and elastic materials, Nat. Rev. Mater. 5, 667 (2020).
  36. J. D. Maynard, Acoustical analogs of condensed-matter problems, Rev. Mod. Phys. 73, 401 (2001).
  37. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Fano resonances in nanoscale structures, Rev. Mod. Phys. 82, 2257 (2010).
  38. S. E. Harris, Electromagnetically induced transparency, Phys. Today 50(7), 36 (1997).
  39. K. L. Johnson and K. L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, UK, 1987).
  40. L. Brillouin, Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices, 2nd ed. (Dover Publications, New York, NY, 1953), originally published in 1946 by McGraw-Hill.
  41. D. J. Inman and R. C. Singh, Engineering Vibration (Prentice Hall, Englewood Cliffs, NJ, 1994), Vol. 3.
  42. H. Yasuda, E. G. Charalampidis, P. K. Purohit, P. G. Kevrekidis, and J. R. Raney, Wave manipulation using a bistable chain with reversible impurities, Phys. Rev. E 104, 054209 (2021).
  43. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Electromagnetically induced transparency: Optics in coherent media, Rev. Mod. Phys. 77, 633 (2005).
  44. M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, Fano resonances in photonics, Nat. Photonics 11, 543 (2017).
  45. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Coupled-resonator-induced transparency, Phys. Rev. A 69, 063804 (2004).
  46. M. F. Yanik, W. Suh, Z. Wang, and S. Fan, Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency, Phys. Rev. Lett. 93, 233903 (2004).

Outline

Information

Phys. Rev. E 114, 035503– Published 4 September, 2026
  • Received 24 May 2026
  • Accepted 30 June 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation