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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.

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.

Analytical treatment of the transient motion of inertial beams attached to coupling inertial resonators (2021)
Journal Article
Nieves, M., & Carta, G. (2021). Analytical treatment of the transient motion of inertial beams attached to coupling inertial resonators. Journal of Engineering Mathematics, 127, Article 20. https://doi.org/10.1007/s10665-021-10110-w

This paper presents, for the first time, an analytical formulation to determine the transient response of an elastic beam possessing distributed inertia and connected to a coupling inertial resonator, represented by a gyroscopic spinner. The latter c... Read More about Analytical treatment of the transient motion of inertial beams attached to coupling inertial resonators.

Directional Control of Rayleigh Wave Propagation in an Elastic Lattice by Gyroscopic Effects (2021)
Journal Article
Nieves, M., Carta, G., Pagneux, V., & Brun, M. (2021). Directional Control of Rayleigh Wave Propagation in an Elastic Lattice by Gyroscopic Effects. Frontiers in Materials, https://doi.org/10.3389/fmats.2020.602960

<jats:p>We discuss the propagation of Rayleigh waves at the boundary of a semi-infinite elastic lattice connected to a system of gyroscopic spinners. We present the derivation of the analytical solution of the equations governing the system when the... Read More about Directional Control of Rayleigh Wave Propagation in an Elastic Lattice by Gyroscopic Effects.

Rayleigh waves in micro-structured elastic systems: Non-reciprocity and energy symmetry breaking (2020)
Journal Article
Nieves, M., Carta, G., Pagneux, V., & Brun, M. (2020). Rayleigh waves in micro-structured elastic systems: Non-reciprocity and energy symmetry breaking. International Journal of Engineering Science, https://doi.org/10.1016/j.ijengsci.2020.103365

Rayleigh waves are analysed in elastic lattices incorporating inertial devices that couple in-plane displacements. The vector problems of elasticity for a triangular lattice and its long-wavelength/low-frequency continuum approximation are considered... Read More about Rayleigh waves in micro-structured elastic systems: Non-reciprocity and energy symmetry breaking.

Reinvigorating the Wiener-Hopf technique in the pursuit to understand processes and materials (2020)
Journal Article
Abrahams, D., Huang, X., Kisil, A., Mishuris, G., Nieves, M., Rogosin, S., & Spitkovsky, I. (2020). Reinvigorating the Wiener-Hopf technique in the pursuit to understand processes and materials. National Science Review, https://doi.org/10.1093/nsr/nwaa225

This perspective originated during the Isaac Newton Institute for Mathematical Sciences research programme “Bringing pure and applied analysis together via the Wiener-Hopf technique, its generalisations and applications (WHT)”. It fuelled intensive d... Read More about Reinvigorating the Wiener-Hopf technique in the pursuit to understand processes and materials.

Dynamic phenomena and crack propagation in dissimilar elastic lattices (2020)
Journal Article
Piccolroaz, A., Gorbushin, N., Mishuris, G., & Nieves, M. (2020). Dynamic phenomena and crack propagation in dissimilar elastic lattices. International Journal of Engineering Science, 103208 - 103208. https://doi.org/10.1016/j.ijengsci.2019.103208

Dynamic Mode III interfacial fracture in a dissimilar square-cell lattice, composed of two contrasting mass-spring lattice half-planes joined at an interface, is considered. The fracture, driven by a remotely applied load, is assumed to propagate at... Read More about Dynamic phenomena and crack propagation in dissimilar elastic lattices.

Flexural vibration systems with gyroscopic spinners. (2019)
Journal Article
Carta, G., Nieves, M. J., Jones, I., Movchan, N., & Movchan, A. (2019). Flexural vibration systems with gyroscopic spinners. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 20190154 - ?. https://doi.org/10.1098/rsta.2019.0154

In this paper, we study the spectral properties of a finite system of flexural elements connected by gyroscopic spinners. We determine how the eigenfrequencies and eigenmodes of the system depend on the gyricity of the spinners. In addition, we prese... Read More about Flexural vibration systems with gyroscopic spinners..

Transient response of a gyro-elastic structured medium: Unidirectional waveforms and cloaking (2019)
Journal Article
Garau, M., Nieves, M. J., Carta, G., & Brun, M. (2019). Transient response of a gyro-elastic structured medium: Unidirectional waveforms and cloaking. International Journal of Engineering Science, 115 - 141. https://doi.org/10.1016/j.ijengsci.2019.05.007

The transient analysis of gyro-elastic structured media, composed of periodically placed masses interconnected by elastic rods and attached to gyroscopic spinners, is presented. The analysis is based on an asymptotic transient model, developed in thi... Read More about Transient response of a gyro-elastic structured medium: Unidirectional waveforms and cloaking.

Dynamic characterization of a periodic microstructured flexural system with rotational inertia. (2019)
Journal Article
Nieves, M. J., & Brun, M. (2019). Dynamic characterization of a periodic microstructured flexural system with rotational inertia. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 20190113 - ?. https://doi.org/10.1098/rsta.2019.0113

We consider the propagation of waves in a flexural medium composed of massless beams joining a periodic array of elements, elastically supported and possessing mass and rotational inertia. The dispersion properties of the system are determined and th... Read More about Dynamic characterization of a periodic microstructured flexural system with rotational inertia..

Alternating Strain Regimes for Failure Propagation in Flexural Systems (2019)
Journal Article
Garau, M., Nieves, M. J., & Jones, I. S. (2019). Alternating Strain Regimes for Failure Propagation in Flexural Systems. Quarterly Journal of Mechanics and Applied Mathematics, 305 - 339. https://doi.org/10.1093/qjmam/hbz008

We consider both analytical and numerical studies of a steady-state fracture process inside a discrete mass-beam structure, composed of periodically placed masses connected by Euler–Bernoulli beams. A fault inside the structure is assumed to propagat... Read More about Alternating Strain Regimes for Failure Propagation in Flexural Systems.

Vibrations and elastic waves in chiral multi-structures (2018)
Journal Article
Nieves, M., Carta, G., Jones, I., Movchan, A., & Movchan, N. (2018). Vibrations and elastic waves in chiral multi-structures. Journal of the Mechanics and Physics of Solids, 387-408. https://doi.org/10.1016/j.jmps.2018.07.020

We develop a new asymptotic model of the dynamic interaction between an elastic structure and a system of gyroscopic spinners that make the overall multi-structure chiral. An important result is the derivation and analysis of effective chiral boundar... Read More about Vibrations and elastic waves in chiral multi-structures.

Design of a chiral elastic structure supporting interfacial waveforms (2018)
Journal Article
Nieves, M., Garau, M., Carta, G., Jones, I., Movchan, N., & Movchan, A. (2018). Design of a chiral elastic structure supporting interfacial waveforms. https://doi.org/10.1109/MetaMaterials.2018.8534138

An infinite heterogeneous elastic triangular lattice connected to a non-uniform array of gyroscopic spinners is considered. An algorithm is described for generating interfacial waves that propagate along the boundaries of subdomains containing inhomo... Read More about Design of a chiral elastic structure supporting interfacial waveforms.

Interfacial waveforms in chiral lattices with gyroscopic spinners (2018)
Journal Article
Garau, M., Carta, G., Nieves, M., Jones, I., Movchan, N., & Movchan, A. (2018). Interfacial waveforms in chiral lattices with gyroscopic spinners. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474(2215), https://doi.org/10.1098/rspa.2018.0132

We demonstrate a new method of achieving topologically protected states in an elastic hexagonal system of trusses by attaching gyroscopic spinners, which bring chirality to the system. Dispersive features of this medium are investigated in detail, an... Read More about Interfacial waveforms in chiral lattices with gyroscopic spinners.