Phononic crystals and elastodynamics: Some relevant points

Abstract

In the present paper we review briefly some of the first works on wave propagation in phononic crystals emphasizing the conditions for the creation of acoustic band-gaps and the role of resonances to the band-gap creation. We show that useful conclusions in the analysis of phononic band gap structures can be drawn by considering the mathematical similarities of the basic classical wave equation (Helmholtz equation) with Schrödinger equation and by employing basic solid state physics concepts and conclusions regarding electronic waves. In the second part of the paper we demonstrate the potential of phononic systems to be used as elastic metamaterials. This is done by demonstrating negative refraction in phononic crystals and subwavelength waveguiding in a linear chain of elastic inclusions, and by proposing a novel structure with close to pentamode behavior. Finally the potential of phononic structures to be used in liquid sensor applications is discussed and demonstrated.

Fully-disposable multilayered phononic crystal liquid sensor with symmetry reduction and a resonant cavity

“…Crystals with a cermet topology are also called acoustic phononic crystals and are composed of a liquid matrix and embedded solid scatterers with high density. On the other hand, crystals with a network topology, or elastic phononic crystals, have a solid matrix and low-density scattering units [6,7].…”

Surface acoustic wave modes in two-dimensional shallow void inclusion phononic crystals on GaAs

“…This bandgap is relatively small compared to the band edge frequencies. Generally, this can be expected for non-hybrid, zone boundary bandgaps [14], and to a lesser extent due to the a solid matrix with less dense solid inclusions [44], and similar results have been observed for SAWs in PnCs with both deep but low elastic contrast [25] and shallow inclusions with high elastic contrast void inclusions [28]. The dispersion shows negative group velocity down to a reduced wavevector of about 0.83, a threshold at which the modes of smaller wavevector are seen to have a hybridized behavior illustrated in Figure 3 (g).…”

Large scale phononic metamaterials for seismic isolation

“…16 Finocchio et al introduced a seismic metamaterial composed of a chain of mass-in-mass system, which is able to filter the S-waves of an earthquake. 17 Aravantinos-Zafiris et al 18 reported results for a new layer-by-layer structure, which was studied as a candidate for pentamode behavior and other interesting elastic metamaterial properties. The structure had a simple cubic symmetry with connecting silicon rods, and it was an easy to fabricate structure.…”

“…Figure 10 of Ref. 18 shows the threedimensional structure. Transferring the idea of this metamaterial to a larger scale could give very useful and promising results in the area of seismic isolation.…”