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Elastodynamics on graphs: wave propagation on networks of plates

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

Authors

Cerian Brewer

GREGOR TANNER GREGOR.TANNER@NOTTINGHAM.AC.UK
Professor of Applied Mathematics



Abstract

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.

Journal Article Type Article
Publication Date Nov 2, 2018
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
APA6 Citation 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), doi:10.1088/1751-8121/aae1d2. ISSN 1751-8113
DOI https://doi.org/10.1088/1751-8121/aae1d2
Keywords Modelling and Simulation; Statistics and Probability; Mathematical Physics; General Physics and Astronomy; Statistical and Nonlinear Physics
Publisher URL http://iopscience.iop.org/article/10.1088/1751-8121/aae1d2/meta
Additional Information Journal title: Journal of Physics A: Mathematical and Theoretical; Article type: paper; Article title: Elastodynamics on graphs—wave propagation on networks of plates; Copyright information: © 2018 IOP Publishing Ltd; Date received: 2018-05-14; Date accepted: 2018-09-17; Online publication date: 2018-10-03

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