Abstract
We construct a family of periodic elastic waveguides Π h , depending on a small geometrical parameter, with the following property: as h → +0, the number of gaps in the essential spectrum of the elasticity system on Π h grows unboundedly.
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Acknowledgements
The first author was partially supported by the Academy of Finland grant no. 127245 and by RFFI, grant 09-01-00759. The third author was partially supported by the Väisälä Foundation of the Finnish Academy of Science and Letters.