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Elastodynamics on graphs: wave propagation on networks of plates

Brewer, Cerian; Creagh, Stephen C.; Tanner, Gregor

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Cerian Brewer

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Professor of Applied Mathematics


We consider the wave dynamics on networks of plates coupled along 1D joints. This set-up can be mapped onto an extension of wave graph systems studied in, for example, quantum graph theory. In the elastic case, different mode-types (flexural, longitudinal and shear waves) propagate in each plate and do so at different wave speeds. The flexural (or bending) modes are described in terms of fourth order equations introducing an always evanescent wave component into the system. Waves encounter plate intersections and can be transmitted, reflected or mode converted. The intersection or vertex scattering matrices mix different waves which can be propagating (open) and evanescent (closed). The local scattering matrices and the global transfer operator are no longer unitary; the consequences of this non-unitarity on secular equations and the Weyl law will be discussed. The findings are of relevance to describing complex engineering structures such as networks of beams and plates.


Brewer, C., Creagh, S. C., & Tanner, G. (2018). Elastodynamics on graphs: wave propagation on networks of plates. Journal of Physics A: Mathematical and Theoretical, 51(44), Article 445101.

Journal Article Type Article
Acceptance Date Sep 17, 2018
Online Publication Date Oct 3, 2018
Publication Date Nov 2, 2018
Deposit Date Oct 23, 2018
Publicly Available Date Oct 4, 2019
Journal Journal of Physics A: Mathematical and Theoretical
Print ISSN 1751-8113
Electronic ISSN 1751-8121
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 51
Issue 44
Article Number 445101
Keywords Modelling and Simulation; Statistics and Probability; Mathematical Physics; General Physics and Astronomy; Statistical and Nonlinear Physics
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