Session: 01-01-04: Phononics IV

Paper Number: 77327

Start Time: Friday, 11:45 AM

77327 - Controlling Subwavelength Near Field Torsional Waves Using Locally Resonant Effective Phononic Crystals 

Locally resonant materials have not only expanded wave control of phononic crystals to subwavelength frequency ranges but also introduced novel wave phenomena such as negative effective properties and enhanced damping. Even though locally resonant materials do not need periodicity, most studies use periodic systems since this simplifies the analysis of complex structures through the application of the Bloch theorem. However, the Bloch theorem requires equations of motion with periodic coefficients and this is only true if the system is periodic with lattice vectors in Cartesian coordinates and under a plane wave assumption. This is why most locally resonant studies assume plane wave propagation. Yet, the plane wave assumption is only valid in the far field of a source. In the near field, waves can be cylindrical in 2D or spherical in 3D. In these cases, even if the medium is invariant to radial translations, the equations of motion are not and the Bloch theorem cannot be applied. To address this, a recent study has shown that non-periodic radially-varying material properties can force the equations of motion to have periodic coefficients in the near field, enabling application of Bloch theorem to radially-propagating torsional waves. These systems are termed effective phononic crystals (EPCs) due to the effective periodicity of their equations of motion. Thus far, EPCs have only considered Bragg scattering, and thus subwavelength wave control is not currently possible.

In this study, we show that using a host medium with radially-varying material properties and equally spaced local resonators, we can force the equations of motion of a locally resonant system to have periodic coefficients for radially-propagating torsional waves. Following their Bragg scattering counterparts, we refer to these materials as locally resonant effective phononic crystals (LREPCs). We show that the equations of motion that describe LRPECs are analogous to those of plane waves propagating through bars or strings with local resonators. Thus, typical properties and analysis of these well-studied systems apply to the LREPCs. To demonstrate the utility of LREPCs for radially-propagating waves, we compare it to a material composed of a host medium with constant material properties, which we term the homogenous system (HS). We use finite element simulations to calculate transmission through a 4-unit cell version of both systems.  The results show that the behavior of the LREPC is independent, whereas that of the HS is strongly dependent on radius. In fact, the behavior of the HS is quite different from that of the LRPEC at small radii and asymptotically approximates the LREPC as radius increases. Finally, we calculate ranges of negative dynamic effective properties using finite element simulations. Due to its effective periodicity, the dynamic effective properties of the LREPC are independent of radii and they become negative inside the band gap, just like Cartesian locally resonant systems. However, dynamic effective properties of the HS show strong radius dependence having quite limited negative frequency ranges, particularly at small radii. Although our study considers torsional waves, a similar approach can be used to expand this work to other polarization or non-axisymmetric wave propagation. LREPCs can be used to control radial waves in subwavelength frequency ranges.

Presenting Author: Ignacio Arretche University of Illinois Urbana-Champaign

Authors:

Ignacio Arretche University of Illinois Urbana-Champaign
Kathryn H. Matlack University of Illinois Urbana-Champaign