1ST-ORDER CORRECTIONS TO THE HOMOGENIZED EIGENVALUES OF A PERIODIC COMPOSITE MEDIUM

This paper studies the eigenvalue problem associated with the vibratio n of a composite medium assumed to have a periodic microstructure. The investigation concentrates on the first-order correction to the homog enized eigenvalues. A major difficulty arises due to the interaction o f the periodic microstructure with the boundary of the medium. The way in which the boundary intersects the underlying periodic structure st rongly influences the value of the correction. A rigorous derivation i s given of the eigenvalue correction formula. The properties of the ei genvalue correction are studied in one- and two-dimensional numerical calculations.