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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 \(h \rightarrow 0\).

MSC:

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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