Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

We present a review, through selected illustra- tive examples, of the physics of classical vibrational modes in phononic lattices, which elaborates on the theo- ry, the formalism, the methods, and mainly on the numer- ical and experimental results related to phononic crystals. Most of the topics addressed here, are written in a self- consistent way and they can be read as independent indi- vidual parts.

http://esperia.iesl.forth.gr/~ppm/PUBLICATIONS/ZfKv220p765_2005.pdf

Classical vibrational modes in phononic lattices: theory and experiment

We demonstrate theoretically the simultaneous localization of photons and phonons in the same spatial region by introducing lattice defects in a periodic array of dielectric/elastic material that exhibits gaps for both electromagnetic and elastic waves. Transverse electromagnetic waves, pure shear elastic waves, and mixed shear and dilatation elastic waves were simultaneously localized. The coexistent localization of light and sound can have a strong influence on photon-phonon interactions (i.e., optical cooling) and the possibility of dual acoustic-optical devices that can integrate the management of sound, heat, and light.

Simultaneous localization of photons and phonons in two-dimensional periodic structures

This work presents results on finite-difference time-domain (FDTD) integration of the full three dimensional elastic wave equation in nonhomogenous periodic media, for understanding the propagation and gap existence in these media. Extensive calculations are compared with plane wave expansion (PWE) data for different three dimensional systems consisting of Pb spheres in epoxy matrix forming an fcc lattice. The method of solving the wave equation provides good convergence and the agreement with the PWE method is excellent. The FDTD method, however, can handle cases such as fluids in solids which cannot be treated with the PWE method. Transmission results are presented for the case of Hg spheres in Al with fcc lattice, in order to prove the general use of the FDTD method.

Theoretical study of three dimensional elastic band gaps with the finite-difference time-domain method

This paper presents the development of an acoustic energy harvester using the sonic crystal and the piezoelectric material. A point defect is created by removing a rod from a perfect sonic crystal. The point defect in the sonic crystal acts as a resonant cavity, and the acoustic waves at the resonant frequency of the cavity can be localized in the cavity. The power generation from acoustic energy is based on the effect of the wave localization in the cavity of the sonic crystal and the direct piezoelectric effect of the piezoelectric material.

Acoustic energy harvesting using resonant cavity of a sonic crystal

Using the plane-wave expansion method, we study the propagation of elastic waves through two-dimensional (2-D) periodic composites which exhibit full band gaps for all the polarizations and directions of the displacements. Defect states created inside those band gaps are also studied by disturbing the periodicity of the lattice. Systems exhibiting such kinds of states can be used as acoustical filters.

M. M. Sigalas

Papers

Elastic wave band gaps and defect states in two-dimensional composites