Elastic wave propagation along waveguides in three-dimensional phononic crystals

Abstract

We investigate theoretically using the finite difference time domain method acoustic wave propagation along waveguides in three-dimensional phononic crystals constituted of lead spherical inclusions on a face-centered cubic lattice embedded in an epoxy matrix. The transmission spectra of the perfect phononic crystal for transverse and longitudinal acoustic waves are shown to depend strongly on the direction of propagation. The crystal possesses an absolute band gap. Waveguides oriented along different crystallographic directions, namely the ͗100͘ and ͗111͘ directions, exhibit pass bands in the phononic crystal band gaps for both transverse and longitudinal polarizations.

Wave localization in randomly disordered periodic piezoelectric rods

“…Equation (13) implies that η j denotes the ratio between the eigenvectors of the two consecutive unit cells. The frequency regions corresponding to |η j | = 1 are called frequency passbands and the disturbances whose frequencies are in these regions can propagate through the periodic structures without attenuation.…”

The Three-Dimensional Phononic Crystals

“…falls within the frequency region of the absolute gap of the perfect phononic crystal. This type of waveguiding has been widely studied both theoretically and experimentally in 2D phononic crystals, but we know of only one work [4] that transferred this idea in 3D phononic crystals using the FDTD method in a solid/solid composite (lead spheres in epoxy). An alternative mechanism for waveguiding relying on weak coupling through defects along a chain, known as coupled-cavity waveguide (CCW), will be presented here.…”

“…Waveguiding in 3D phononic crystals has been very little studied up to now [4,49]. Waveguides in phononic-crystal structures are usually created by removing a row (line) of cylinders (spheres), so that the elastic waves of angular frequency !…”

The transmission properties of elastic waves through multilayers of spheres with planar defects

“…(3a) and (3b) represent the transmission amplitude and the reflection amplitude when the incident wave comes from the left side of the layer of spheres; the second terms represent the reflection amplitude and the transmission amplitude when the incident wave comes from the right side of the layer of spheres. For the explicit expressions of the matrix M pq i j refer to [20].…”

“…However, the influences of defects in the three-dimensional composite on the band gap of a periodic structure have been less studied up to now. Chandra et al [20] studied the propagation of acoustical waves along the waveguides existing in three-dimensional composites of spherical lead inclusions. The waveguide structures were constructed by removing a row of inclusions from the perfect crystal along some chosen crystallographic direction.…”