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Rayleigh waves in micro-structured elastic systems: Non-reciprocity and energy symmetry breaking

Nieves

Rayleigh waves in micro-structured elastic systems: Non-reciprocity and energy symmetry breaking Thumbnail


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Abstract

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. The analytical procedure for the derivation of the Rayleigh dispersion relation is fully detailed and, remarkably, explicit solutions for the Rayleigh waves for both the discrete and continuous systems are found. The dispersion at low wavenumbers and the softening induced by the presence of in-plane inertial coupling are shown. Despite the symmetry of the dispersion curves with respect to the wavenumber, the introduction of the inertial coupling breaks the symmetry of the eigenmodes and makes the system non-reciprocal. Such an uncommon effect is demonstrated in a set of numerical computations, where a point force applied on the boundary generates surface and bulk waves that do not propagate symmetrically from the source.

Acceptance Date Jul 27, 2020
Publication Date Nov 1, 2020
Journal International Journal of Engineering Science
Print ISSN 0020-7225
Publisher Elsevier
DOI https://doi.org/10.1016/j.ijengsci.2020.103365
Keywords Rayleigh waves, Micro-structured elastic medium, Mechanical metamaterial, Gyroscopic properties, Non-reciprocity, Energy flow
Publisher URL http://doi.org/10.1016/j.ijengsci.2020.103365

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