Interaction of in-plane waves with a structured penetrable line defect in an elastic lattice

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• Michael Nieves (Keele University)
• Friday 05 July 2024, 11:45-12:15
• Seminar Room 1, Newton Institute.

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WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method

We investigate the scattering of in-plane waves in a triangular elastic lattice by a penetrable inertial line defect [1]. Through the application of the discrete Fourier transform, this problem can be reduced to the analysis of two scalar Wiener-Hopf equations involving the transformed displacements along the defected lattice row. From there, essential information can be extracted about: (i) all dynamic modes appearing in the scattering process, (ii) the symmetry properties of each mode, and (iii) parameter subdomains, defined by the incident wave frequency and inertial properties of the defect, where dynamic localised modes supported by the defect can appear. Upon solving the Wiener-Hopf equations, the lattice displacements can be represented by a contour integral, which can be used to investigate unusual scattering responses of the defect encountered outside of the low frequency regime. All analytical results presented are accompanied by numerical illustrations that demonstrate their effectiveness. Acknowledgement: MJN gratefully acknowledges the support of the EU H2020 grant MSCA -RISE-2020-101008140-EffectFact. MJN would also like to thank the Isaac Newton Institute for Mathematical Sciences (INI) for their support and hospitality during the programme ``Mathematical theory and applications of multiple wave scattering” (MWS), where work on the research in the talk was undertaken and supported by EPSRC grant no. EP/R014604/1. Additionally, MJN is grateful for the funding received from the Simons Foundation that supported his visit to INI during January-June 2023 and participation in MWS programme. References:[1] M.J. Nieves, B.L. Sharma (2024): Interaction of in-plane waves with a structured penetrable line defect in an elastic lattice, Int. J. Eng. Sci 197, 104011, 10.1016/j.ijengsci.2023.104011  

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