On the existence of waves guided by a cavity in an elastic film

Cherednichenko, Kirill and Sabina, F. J. 2009. On the existence of waves guided by a cavity in an elastic film. Quarterly Journal of Mechanics and Applied Mathematics 62 (3) , pp. 221-233. 10.1093/qjmam/hbp007

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Abstract

In the regime where linearised elasticity is a suitable approximation to the behaviour of an elastic body, the existence of a wave guided along the cavity in a film of a homogeneous and isotropic elastic material is proved, at least for a certain range of frequencies. Using the theory of linear self-adjoint operators, it is shown that the associated eigenvalue problem has a nontrivial solution in an appropriate Sobolev class, with the corresponding eigenvalue lying below the continuous spectrum. We study the existence of localised modes of this kind in two particular cases: under the assumption that the cavity is sufficiently narrow in the direction transverse to the film and for a rectangular cavity of arbitrary size.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Oxford University Press
ISSN:	0033-5614
Funders:	EPSRC
Last Modified:	04 Nov 2017 23:39
URI:	https://orca.cardiff.ac.uk/id/eprint/13246

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