Bloch Spectra for High Contrast Elastic Media
Abstract
Analytic representation formulas and power series are developed to describe the band structure inside periodic elastic crystals made from high contrast inclusions. We use source free modes associated with structural spectra to represent the solution operator of the Lamé system inside phononic crystals. Convergent power series for the Bloch wave spectrum are obtained using the representation formulas. An explicit bound on the convergence radius is given through the structural spectra of the inclusion array and the Dirichlet spectra of the inclusions. Sufficient conditions for the separation of spectral branches of the dispersion relation for any fixed quasimomentum are identified.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.08405
 Bibcode:
 2021arXiv211008405L
 Keywords:

 Mathematics  Analysis of PDEs;
 35P05;
 35B34;
 35B40;
 47A10
 EPrint:
 37 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1512.06062