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Band Structure Calculations by Modal Analysis

  • Mahmoud I. Hussein
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 26)

Abstract

In this paper we present a new paradigm by which modal analysis – which is well established in engineering structural dynamics – is applied to band structure calculations for phononic crystals, or periodic media in general. Our method, which we refer to as reduced Bloch mode expansion (RBME), is essentially an expansion employing a natural basis composed of a selected reduced set of Bloch eigenfunctions. This reduced basis is selected within the Irreducible Brillouin Zone at high symmetry points determined by the crystal structure and group theory (and possibly at additional related points). At each of these high symmetry points, a number of Bloch eigenfunctions are selected up to the frequency range of interest for the band structure calculations. Since it is common to initially discretize the problem at hand using some choice of basis, reduced Bloch mode expansion constitutes a secondary expansion using a set of Bloch eigenvectors, and hence keeps and builds on any favorable attributes a primary expansion approach might exhibit. We report phonon band structure calculations by the proposed method showing up to two orders of magnitude reduction in computational effort with negligible loss in accuracy.

Keywords

Photonic Crystal Modal Analysis Band Structure Calculation Phononic Crystal Irreducible Brillouin Zone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Aerospace Engineering SciencesUniversity of Colorado at BoulderBoulderUSA

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