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 \(h \rightarrow 0\).


Elliptic system Linearized elasticity problem Essential spectrum Spectral band Spectral gap Asymptotic analysis Floquet–Bloch theory 

Mathematics Subject Classification

Primary 35J57 Secondary 35P99 35Q74 74J05 


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Authors and Affiliations

  1. 1.Chebyshev LaboratorySt. Petersburg State UniversitySaint PetersburgRussia
  2. 2.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland

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