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SUMMARY:Edge and bulk resonances in structured elastic strips - Dr Michael
  Nieves\, Keele University
DTSTART:20251204T160000Z
DTEND:20251204T180000Z
UID:TALK235282@talks.cam.ac.uk
CONTACT:Dr Matthew Nethercote
DESCRIPTION:We consider waves propagating through elastic triangular latti
 ce strips formed from periodically placed masses interconnected by elastic
  rods. Of particular interest is the behaviour of the strips near resonanc
 e regimes\, which we investigate for (i) a semi-infinite strip and (ii) a 
 strip with gyroscopes attached to its junctions.\n \nIn the first part of 
 the talk\, we discuss the problem of edge resonance for Lamb waves in a se
 mi-infinite discrete elastic strip [1]\, represented by a triangular latti
 ce. In analogy with the reflection problem in the corresponding continuum\
 , for real frequencies the edge resonance phenomenon for the lattice strip
  is characterised by localised vibrations at its free edge. We verify the 
 existence of a complex edge resonance frequency for the lattice\, associat
 ed with a mode of the homogenous problem without incident wave. Importantl
 y\, when the number of rows in the strip of fixed width is large\, we show
  the lattice’s edge resonance frequency approximates corresponding frequ
 ency in the analogous continuum problem for the effective strip. Interesti
 ngly\, convergence to the complex edge resonance frequency is monotonic on
 ly with respect to its real part\, while its imaginary part exhibits a min
 imum absolute value for a lattice strip with 65 rows in the transverse dir
 ection.\n \nIn the second part of the talk\, we consider the gyroscopic el
 astic strip.  The presence of the gyroscopes makes the system non-reciproc
 al. Near a bulk resonance\, this allows the medium to support uni-directio
 nal Lamb waves when subjected to forcing [2]. We discuss the solution to t
 his problem and demonstrate how information related to this can lead to de
 signs of novel waveguides. Namely\, we illustrate how we can create a netw
 ork of structured strips that can channel waves generated by an external s
 ource at one point in the system to any end point in the network\, which c
 an be chosen in advance.\n \nAll analytical results are accompanied by num
 erical simulations illustrating the approaches and their effectiveness whe
 n benchmarked against independent calculations based on the finite element
  method.\n \nReferences:\n \n[1] G. Carta\, M.J.Nieves\, M. Brun\, V. Pagn
 eux (2025): Edge resonance in triangular lattices strips and continuum app
 roximation\, Int. J. Eng. Sci. 215\, 104307.\n\n[2] G. Carta\, M.J.\, Niev
 es\, M. Brun\, (2023): Forcing the Silence of the Lamb waves: Uni-directio
 nal propagation in structured gyro-elastic strips and networks\, Eur. J. M
 ec. A-Solid 101\, 105070
LOCATION:Centre for Mathematical Sciences MR5\, CMS
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