Premium
Acoustic Band Structures and Homogenization of Periodic Elastic Media
Author(s) -
Stadler Michael,
Schanz Martin
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010206
Subject(s) - homogenization (climate) , anisotropy , eigenvalues and eigenvectors , periodic boundary conditions , finite element method , homogeneous , mathematical analysis , solver , boundary value problem , unit square , materials science , frequency band , mathematics , mechanics , physics , mathematical optimization , optics , computer science , statistical physics , thermodynamics , biodiversity , ecology , computer network , bandwidth (computing) , quantum mechanics , biology
Dispersion curves and frequency dependent velocity surfaces of periodic heterogeneous elastic media are determined from unit‐cell problems using quasi periodic boundary conditions. Effective material parameters are obtained using a least square optimization of the phase velocities in the heterogeneous and the effective, generally anisotropic, homogeneous medium. For efficiency, a preconditioned iterative eigenvalue solver and a model order reduction scheme are used. This “dynamic” homogenization procedure is validated for frequencies below the first stop band employing FEM calculations on a finite structure consisting of an array of unit‐cells and the effective homogeneous material. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)