Geodesic
Gap detection in the spectrum of an elastic periodic waveguide with a free surface
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 332-343

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A three-dimensional periodic elastic waveguide is constructed whose continuous spectrum (the frequencies that admit propagating waves) contains a gap, i.e., an interval that has its ends in the continuous spectrum but contains at most a discrete spectrum. The waveguide consists of an infinite chain of massive bodies connected by short thin links, and its surface is assumed to be free. The method for detecting a gap also applies to plane problems, including scalar ones. Periodic elastic waveguides with different shapes or contrasting properties are indicated in which a gap can also be detected. 
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     author = {S. A. Nazarov},
     title = {Gap detection in the spectrum of an elastic periodic waveguide with a~free surface},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {332--343},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a11/}
}
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S. A. Nazarov. Gap detection in the spectrum of an elastic periodic waveguide with a free surface. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 332-343. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a11/