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Edge resonance in discrete elastic waveguides and its convergence to isotropic continuous media (2025)
Journal Article
Carta, G., Nieves, M., Brun, M., & Pagneux, V. (2025). Edge resonance in discrete elastic waveguides and its convergence to isotropic continuous media. International Journal of Engineering Science, 215, Article 104307. https://doi.org/10.1016/j.ijengsci.2025.104307

We discuss the problem of edge resonance for Lamb waves in a semi-infinite discrete elastic strip, represented by a triangular lattice. In analogy with the reflection problem in the corresponding continuum, for real frequencies the edge resonance phe... Read More about Edge resonance in discrete elastic waveguides and its convergence to isotropic continuous media.

Analytical and numerical study of anti-plane elastic wave scattering in a structured quadrant subjected to a boundary point load (2024)
Journal Article
Nieves, M., Kisil, A., & Mishuris, G. S. (in press). Analytical and numerical study of anti-plane elastic wave scattering in a structured quadrant subjected to a boundary point load. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480(2299), Article 20240099. https://doi.org/10.1098/rspa.2024.0099

We verify the recently developed method by Kisil (Kisil 2024 SIAM J. Appl. Math. 84, 464–476 (doi: 10.1137/23M1562445)) through its application in the study of the anti-plane dynamic response of an elastic square-cell lattice quadrant having a free l... Read More about Analytical and numerical study of anti-plane elastic wave scattering in a structured quadrant subjected to a boundary point load.

Interaction of in-plane waves with a structured penetrable line defect in an elastic lattice (2024)
Journal Article
Nieves, M., & Sharma, B. (2024). Interaction of in-plane waves with a structured penetrable line defect in an elastic lattice. International Journal of Engineering Science, 197, Article 104011. https://doi.org/10.1016/j.ijengsci.2023.104011

We consider the scattering of in-plane waves that interact with an edge of a structured penetrable inertial line defect contained in a triangular lattice, composed of periodically placed masses interconnected by massless elastic rods. The steady stat... Read More about Interaction of in-plane waves with a structured penetrable line defect in an elastic lattice.

Forcing the silence of the Lamb waves: Uni-directional propagation in structured gyro-elastic strips and networks (2023)
Journal Article
Carta, G., Nieves, M., & Brun, M. (2023). Forcing the silence of the Lamb waves: Uni-directional propagation in structured gyro-elastic strips and networks. European Journal of Mechanics - A/Solids, 101, Article 105070. https://doi.org/10.1016/j.euromechsol.2023.105070

In this paper, we propose an innovative design of an elastic network, which is capable of channelling the energy supplied by an external source towards any of its endpoints, that can be chosen arbitrarily and in advance. This system, named Mechanical... Read More about Forcing the silence of the Lamb waves: Uni-directional propagation in structured gyro-elastic strips and networks.

Asymptotic Theory of Generalised Rayleigh Beams and the Dynamic Coupling (2023)
Presentation / Conference Contribution
Nieves, M. J., & Movchan, A. B. (2023, April). Asymptotic Theory of Generalised Rayleigh Beams and the Dynamic Coupling

We consider the effective dynamic response of an infinite asymmetric structure formed from a beam attached to a periodic array of resonators. The array couples the axial and flexural motions of the beam. We develop a point-wise description of the res... Read More about Asymptotic Theory of Generalised Rayleigh Beams and the Dynamic Coupling.

Dynamic fracture regimes for initially prestressed elastic chains. (2022)
Journal Article
Nieves. (2022). Dynamic fracture regimes for initially prestressed elastic chains. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 20210395 - ?. https://doi.org/10.1098/rsta.2021.0395

We study the propagation of a bridge crack in an anisotropic multi-scale system involving two discrete elastic chains that are interconnected by links and possess periodically distributed inertia. The bridge crack is represented by the destruction of... Read More about Dynamic fracture regimes for initially prestressed elastic chains..

Asymptotic analysis of in-plane dynamic problems for elastic media with rigid clusters of small inclusions. (2022)
Journal Article
Nieves. (2022). Asymptotic analysis of in-plane dynamic problems for elastic media with rigid clusters of small inclusions. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, -. https://doi.org/10.1098/rsta.2021.0392

We present formal asymptotic approximations of fields representing the in-plane dynamic response of elastic solids containing clusters of closely interacting small rigid inclusions. For finite densely perforated bodies, the asymptotic scheme is devel... Read More about Asymptotic analysis of in-plane dynamic problems for elastic media with rigid clusters of small inclusions..

Meso-scale method of asymptotic analysis of elastic vibrations in periodic and non-periodic multi-structures (2022)
Journal Article
Nieves, M. J., & Movchan, A. B. (2022). Meso-scale method of asymptotic analysis of elastic vibrations in periodic and non-periodic multi-structures. Quarterly Journal of Mechanics and Applied Mathematics, 75(3), 171 - 214. https://doi.org/10.1093/qjmam/hbac011

<jats:title>Summary</jats:title> <jats:p>The method of meso-scale asymptotic approximations has proved to be very effective for the analysis of models of solids containing large clusters of defects, such as small inclusions or voids. Here, we present... Read More about Meso-scale method of asymptotic analysis of elastic vibrations in periodic and non-periodic multi-structures.

On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions (2021)
Journal Article
Maz′ya, V., Movchan, A., & Nieves, M. (2021). On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions. St. Petersburg Mathematical Journal, 32(3), 551 - 564. https://doi.org/10.1090/spmj/1661

Formal asymptotic algorithms are considered for a class of meso-scale approximations for problems of vibration of elastic membranes that contain clusters of small inertial inclusions distributed along contours of predefined smooth shapes. Effective t... Read More about On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions.