Bands in the spectrum of a periodic elastic waveguide. (English) Zbl 1378.35295

Summary: 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 \(h \rightarrow 0\).


35Q74 PDEs in connection with mechanics of deformable solids
35J57 Boundary value problems for second-order elliptic systems
74J05 Linear waves in solid mechanics
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