Archive for Rational Mechanics and Analysis

, Volume 171, Issue 1, pp 129-150

First online:

Analysis of Elastic Band Structures for Oblique Incidence

  • S. GuenneauAffiliated withDepartment of Physics, Imperial College
  • , A.B. MovchanAffiliated withDepartment of Mathematical Sciences, University of Liverpool Email author 

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We propose a canonical basis that is used in the expansion of eigensolutions for a problem of oblique incidence of elastic waves on a doubly periodic array of cylindrical channels. We apply a multipole method to study the spectral properties of waves in such a structure. Dispersion diagrams constructed on the basis of an analytical solution show the presence of a full phononic band gap when the angle of oblique incidence exceeds certain critical value. Explicit asymptotic formulae are presented for the effective refractive index associated with shear waves in oblique incidence.