Edge and bulk resonances in structured elastic strips

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• Dr Michael Nieves, Keele University
• Thursday 04 December 2025, 16:00-18:00
• Centre for Mathematical Sciences MR5, CMS.

If you have a question about this talk, please contact Dr Matthew Nethercote.

We consider waves propagating through elastic triangular lattice strips formed from periodically placed masses interconnected by elastic rods. Of particular interest is the behaviour of the strips near resonance regimes, which we investigate for (i) a semi-infinite strip and (ii) a strip with gyroscopes attached to its junctions.

In the first part of the talk, we discuss the problem of edge resonance for Lamb waves in a semi-infinite discrete elastic strip [1], represented by a triangular lattice. 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, associated with a mode of the homogenous problem without incident wave. Importantly, when the number of rows in the strip of fixed width is large, we show the lattice’s edge resonance frequency approximates corresponding frequency in the analogous continuum problem for the effective strip. Interestingly, convergence to the complex edge resonance frequency is monotonic only with respect to its real part, while its imaginary part exhibits a minimum absolute value for a lattice strip with 65 rows in the transverse direction.

In the second part of the talk, we consider the gyroscopic elastic strip. The presence of the gyroscopes makes the system non-reciprocal. Near a bulk resonance, this allows the medium to support uni-directional Lamb waves when subjected to forcing [2]. We discuss the solution to this problem and demonstrate how information related to this can lead to designs of novel waveguides. Namely, we illustrate how we can create a network of structured strips that can channel waves generated by an external source at one point in the system to any end point in the network, which can be chosen in advance.

All analytical results are accompanied by numerical simulations illustrating the approaches and their effectiveness when benchmarked against independent calculations based on the finite element method.

References:

[1] G. Carta, M.J.Nieves, M. Brun, V. Pagneux (2025): Edge resonance in triangular lattices strips and continuum approximation, Int. J. Eng. Sci. 215, 104307.

[2] G. Carta, M.J., Nieves, M. Brun, (2023): Forcing the Silence of the Lamb waves: Uni-directional propagation in structured gyro-elastic strips and networks, Eur. J. Mec. A-Solid 101, 105070

This talk is part of the Waves group seminar series.

This talk is included in these lists:

• Centre for Mathematical Sciences MR5, CMS
• Waves group seminar

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