Nonlinear elastic wave propagation in a phononic material with periodic solid–solid contact interface

I. Grinberg, K. H. Matlack

Research output: Contribution to journalArticlepeer-review


Phononic materials enable enhanced dynamic properties, and offer the ability to engineer the material response. In this work we study the wave propagation in such a structure when introduced with nonlinearity. Our system is comprised of pre-compressed material with periodic solid–solid contacts, which exhibit a quadratic nonlinearity for small displacements. We suggest a new approach to modeling this system, where we discretize the unit cell in order to derive an approximate analytical solution using a perturbation method, which we are then able to easily validate numerically. With these methods, we study the band structure in the system and the second harmonic generation originating from the nonlinearity. We qualitatively analyze the second harmonic response of the system in terms of the single-crack response with linear band structure considerations. Significant band structure manipulation by changing system parameters is demonstrated, including possible in-situ tuning. The system also exhibits effective frequency doubling, i.e. the transmitted wave is primarily comprised of the second harmonic wave, for a certain range of frequencies. We demonstrate very high robustness to disorder in the system, in terms of band structure and second harmonic generation. These results have possible applications as frequency-converting devices, tunable engineered materials, and in non-destructive evaluation.

Original languageEnglish (US)
Article number102466
JournalWave Motion
StatePublished - Jan 2020


  • Contact interfaces
  • Frequency doubling
  • Nonlinearity
  • Phononic material
  • Second harmonic generation

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Physics and Astronomy
  • Computational Mathematics
  • Applied Mathematics


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