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SUMMARY:Interaction of in-plane waves with a structured penetrable line de
 fect in an elastic lattice - Michael Nieves (Keele University)
DTSTART:20240705T104500Z
DTEND:20240705T111500Z
UID:TALK215011@talks.cam.ac.uk
DESCRIPTION:We investigate the scattering of in-plane waves in a triangula
 r elastic lattice by a penetrable inertial line defect [1]. Through the ap
 plication of the discrete Fourier transform\, this problem can be reduced 
 to the analysis of two scalar Wiener-Hopf equations involving the transfor
 med displacements along the defected lattice row. From there\, essential i
 nformation 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 inertia
 l properties of the defect\, where dynamic localised modes supported by th
 e 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 out
 side of the low frequency regime. All analytical results presented are acc
 ompanied by numerical illustrations that demonstrate their effectiveness.\
 nAcknowledgement: MJN gratefully acknowledges the support of the EU H2020 
 grant MSCA-RISE-2020-101008140-EffectFact. MJN would also like to thank th
 e Isaac Newton Institute for Mathematical Sciences (INI) for their support
  and hospitality during the programme ``Mathematical theory and applicatio
 ns of multiple wave scattering" (MWS)\, where work on the research in the 
 talk was undertaken and supported by EPSRC grant no. EP/R014604/1. Additio
 nally\, MJN is grateful for the funding received from the Simons Foundatio
 n that supported his visit to INI during January-June 2023 and participati
 on in MWS programme.\nReferences:[1] M.J. Nieves\, B.L. Sharma (2024): Int
 eraction 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&nbsp\;&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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