### Abstract

Language | English |
---|---|

Pages | 1 - 16 |

Number of pages | 16 |

Journal | Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences |

Volume | 471 |

Issue number | 2178 |

Early online date | 13 May 2015 |

DOIs | |

Status | Published - Jun 2015 |

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### Cite this

**On the existence of high-frequency boundary resonances in layered elastic media.** / Cherednichenko, Kirill; Cooper, Shane.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences*, vol 471, no. 2178, pp. 1 - 16. DOI: 10.1098/rspa.2014.0878

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TY - JOUR

T1 - On the existence of high-frequency boundary resonances in layered elastic media

AU - Cherednichenko,Kirill

AU - Cooper,Shane

PY - 2015/6

Y1 - 2015/6

N2 - We analyse the asymptotic behaviour of high-frequency vibrations of a three-dimensional layered elastic medium occupying the domain Ω=(−a,a)3, a>0. We show that in both cases of stress-free and zero-displacement boundary conditions on the boundary of Ω a version of the boundary spectrum, introduced in Allaire and Conca (1998 J. Math. Pures. Appl. 77, 153–208. (doi:10.1016/S0021-7824(98)80068-8)), is non-empty and part of it is located below the Bloch spectrum. For zero-displacement boundary conditions, this yields a new type of surface wave, which is absent in the case of a homogeneous medium.

AB - We analyse the asymptotic behaviour of high-frequency vibrations of a three-dimensional layered elastic medium occupying the domain Ω=(−a,a)3, a>0. We show that in both cases of stress-free and zero-displacement boundary conditions on the boundary of Ω a version of the boundary spectrum, introduced in Allaire and Conca (1998 J. Math. Pures. Appl. 77, 153–208. (doi:10.1016/S0021-7824(98)80068-8)), is non-empty and part of it is located below the Bloch spectrum. For zero-displacement boundary conditions, this yields a new type of surface wave, which is absent in the case of a homogeneous medium.

UR - http://dx.doi.org/10.1098/rspa.2014.0878

U2 - 10.1098/rspa.2014.0878

DO - 10.1098/rspa.2014.0878

M3 - Article

VL - 471

SP - 1

EP - 16

JO - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

T2 - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

SN - 1364-503X

IS - 2178

ER -