Bands in the spectrum of a periodic elastic waveguide
  We study the spectral linear elasticity problem in an unbounded periodic waveguide, which consists of a sequence of identical bounded cells connected by thin ligaments of diameter of order $ h >0$. The essential spectrum of the problem is known to have band-gap structure. We derive asymptotic formulas for the position of the spectral bands and gaps, as $h \to 0$. 
F.L. Bakharev and J. Taskinen
math.SP math.AP