Elastodynamics on graphs: wave propagation on networks of plates

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

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.

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), Article 445101. https://doi.org/10.1088/1751-8121/aae1d2

• 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
• 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
• Public URL: https://nottingham-repository.worktribe.com/output/1181476
• Publisher URL: http://iopscience.iop.org/article/10.1088/1751-8121/aae1d2/meta