Waves control

Phononic crystals have attracted significant interest for the development of devices that exhibit, among others, acoustic super-lensing, super-focusing and cloaking characteristics. Their interesting properties rely on the ability to tailor the propagation of acoustic waves through bandgaps: frequency ranges where wave propagation is forbidden. Bandgaps are the result of wave scattering at periodic impedance mismatch zones (Bragg scattering) and  are exploited  to filter, localize and guide acoustic waves.

Most of the phononic crystals proposed so far operate at fixed frequency ranges. The design of phononic crystals capable of changing their frequency bandgaps through an external stimulus remains an outstanding challenge for the development of next-generation acoustic devices. We  exploit external stimuli that induce large deformations and trigger local instabilities in the structure to tune the functionalities of phononic crystals.

We found that the pattern transformations occurring at instability  strongly affect the phononic band gaps of the material. At instability, some of the pre-existing band gaps close and new ones open, leading to interesting applications in phononic crystals. Specifically this effect could be used to fabricate acoustic switches to filter sound in a controlled manner. For 2D periodic porous structures microscopic instabilities have been shown to persist also at the sub-micron scale, inducing significant changes in the optical transmittance of photonic crystals.

Phononic band-gap structure and wave directionality for a square array of circular void in an elastic matrix subjected to uniaxial compression at different levels of  deformation.  

Furthermore, periodic cellular structures are also characterized by a low frequency directional behavior that  can be exploited to steer or redirect waves in specific directions. The directionality is determined by the level of anisotropy of the structure and can be fully controlled through proper arrangement of the material distribution at the unit cell level. Our recent  results for low amplitude waves propagating in a square array of circular voids indicate that the topological changes induce by instabilities have a significant effect on the wave directionality. The wave speed polar diagram for the undeformed (before buckling) configuration clearly shows a lobed pattern with maxima oriented at 0o and 45o degrees for the shear and pressure mode, respectively. These maxima clearly indicate preferential directions for the propagation of waves within the structure and are strongly related to the anisotropy of the microstructure. By contrast, after buckling the system behaves as an isotropic medium for waves propagating in the considered frequency range.

Our analyses have not been limited to 2D periodic structures, but we also investigated the effect on wave propagation of instabilities occurring in 3D structures and granular crystals. Furthermore, we recently purchased the equipment required for vibration testing, including shakers, accelerometers and an acquisition system.


  • Wang P, Casadei F, Shan S, Weaver JC, Bertoldi K. Harnessing Buckling to Design Tunable Locally Resonant Acoustic Metamaterials. Physical Review Letters. 2014;113:014301.
  • Casadei F, Bertoldi K. Harnessing fluid-structure interactions to design self-regulating acoustic metamaterials. Journal of Applied Physics. 2014;115:034907.
  • Wang P, Shim J, Bertoldi K. E ffects of Geometric and Material Non-linearities on the Tunable Response of Phononic Crystals. Physical Review B. 2013;88:014304.
  • F. Goncu, S. Luding and K. Bertoldi. Exploiting pattern transformation to tune phononic band gaps in a two-dimensional granular crystal. Journal of the Acoustical Society of America, 131: EL475-EL480, 2012.
  • L. Wang and K. Bertoldi. Mechanically tunable phononic band gaps in three-dimensional periodic elastomeric structures. International Journal of Solids and Structures, 49: 2881-2885, 2012.
  • J. Li, J. Shim, J. Deng, J.T.B. Overvelde, X. Zhu, K. Bertoldi and S. Yang. Switching periodic membranes via pattern transformation and shape memory effect. Soft Matter, 8: 10322-10328, 2012.