Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates

Abstract

We introduce a supercell plane wave expansion ͑SC-PWE͒ method for the calculation of elastic band structures of two-dimensional phononic crystal plates. We compute the band structure of solid-solid and air-solid two-dimensional phononic crystal plates. The air is modeled as a low impedance medium ͑LIM͒ with very low density and very high velocities of sound. We investigate the influence of the constituent materials, of the plate thickness, and of the geometry of the array on the band structure. We establish the range of validity of the SC-PWE method in terms of the rate of convergence with respect to the number of plane waves and contrast in physical properties of the matrix and inclusion materials. We show that for high contrast solid-solid phononic crystal plates, our SC-PWE method, as other PWE-based methods introduced to date, suffers from convergence difficulties. In the case of air ͑modeled as the LIM͒ holes-solid plates, we demonstrate that the SC-PWE method leads to fast convergence for a wide range of values of solid physical properties. With these constituent materials, we find that the largest absolute forbidden bands occur in the band structure of the phononic crystal plate provided the thickness of the plate is of the order of magnitude of the periodicity of the array of inclusions. We demonstrate the existence of guided modes in an air-silicon phononic crystal plate containing a linear defect.

Thermal transport in phononic crystals and the observation of coherent phonon scattering at room temperature

“…8). It is particularly interesting that the hybrid model agrees well with the experimental data when the TMFP is large enough to cover 3-5 lattice periods, as this is similar to the literature-accepted bounds 10,[33][34][35][36][37][38][39] for the fewest and largest number of periods needed to observe PnC behaviour.…”

Evanescent waves and deaf bands in sonic crystals

“…This results in a periodic arrangement of supercells which contains the point defect. With this method it is possible to obtain the relation ω( k) for crystals with local defects and for instance one can explain the physics of wave guides 29,30 or filters. 31 In this Section, we apply the approximation of supercell to the EPWE.…”

Numerical Evaluation of Sound Attenuation Provided by Periodic Structures

“…In the first group, aspects such as the influence of so called point defects (Wu et al, 2009) or the existence of waveguides in which the sound propagates with low attenuation (Vasseur et al, 2008) can be mentioned. In the field of the practical uses of sonic crystals, one which may be regarded perhaps as the most promising is their precise use for the selective attenuation of sound, for example as traffic noise barriers (Sánchez-Pérez et al, 2002).…”