Band structure and eigenmodes of two-dimensional phononic crystals

A general approach to analysis of the eigenmodes of phononic crystals with arbitrary anisotropy and unit cell geometry is proposed. The proposed approach is based on the operator representation of the equation for a stationary elastic wave in a continuous medium. It is shown that this operator equation reduces to a matrix problem of finding the eigenvalues and eigenvectors of the matrix. The developed theory was used to calculate the band structure and the spatial distributions of displacement fields in a two-dimensional phononic crystal. The influence of the parameters of a two-dimensional phononic crystal on the dispersion of its eigenmodes was studied. Effects associated with the polarization of elastic waves were analyzed.

Authors: Z. M. Yashkin, M. V. Zakharchenko, G. F. Glinskii

Direction: Physics

Keywords: band structure of phononic crystal, anisotropy of elastic properties, polarization of elastic waves

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