Title   name
KSIAM 2006 Annual Meeting
 
  Title
  Speaker   Lee, Hyundae  
  Date 2006-11-25
  Host
  Place 건국대학교
  File  의 1 번째 Real Media 동영상입니다. 의 1 번째 강연자료입니다.
 
Abstract : We investigate the band-gap structure of the frequency spectrum for elastic waves in a highcontrast,two-component periodic elastic medium.We consider two-dimensional phononic crystalsconsisting of a background medium which is perforated by an array of holes periodic alongeach of the two orthogonal coordinate axes. In this paper we establish a full asymptotic formulafor dispersion relations of phononic band structures. The main ingredients are integral equationformulations of the solutions to the harmonic oscillatory linear elastic equation and severaltheorems concerning the characteristic values of meromorphic operator-valued functions in thecomplex plane such as Generalized Rouch´e’s theorem. We establish a connection between theband structures and the Dirichlet eigenvalue problem on the elementary hole. We also providea criterion for exhibiting gaps in the band structure which shows that smaller the density of thematrix is, wider the band-gap is, provided that the criterion is fulfilled. This phenomenon wasreported by Economou and Sigalas in [15] who observed that periodic elastic composites whosematrix has lower density and higher shear modulus compared to those of inclusions yield betteropen gaps. Our analysis in this paper agrees with this experimental finding.