On the existence of high-frequency boundary resonances in layered elastic media
Kirill Cherednichenko, Shane Cooper · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2015
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.