Elastic Wave Mode Conversion Exploiting Anisotropic Locally Resonant Metamaterials
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Locally resonant metamaterials (LRMs) are a promising class of engineered materials for elastic wave manipulation, typically consisting of periodically distributed resonant elements, e.g., soft inclusions embedded in a stiff matrix. The interaction between propagating elastic waves and the local resonances of the inclusions leads to the formation of band gaps, which can be interpreted as frequency intervals associated with negative effective mass density. When inclusions lack rotational symmetry, the effective mass density of the media becomes anisotropic, unlocking additional features in LRMs. Through proper design of the resonators, it is possible to achieve negative refraction [1] and the formation of polarization bands [2], where selective wave polarization and mode conversion can be achieved. In [3], we showed that asymptotic homogenization can be effectively employed to characterize the effective properties of anisotropic LRMs. In particular, we studied how the formation of pass bands, polarization bands and band gaps is strictly related to the spectral properties of the homogenized mass density tensor of the metamaterial. In this work, we consider a homogeneous, linear-elastic, isotropic medium in which periodically distributed elliptical soft inclusions are embedded in a central strip only. By means of a semi-analytical solution based on homogenization and of numerical analyses, we show how an incoming longitudinal wave can be converted into a shear one when travelling through the anisotropic LRM. The results confirm the capability of anisotropic LRMs to achieve mode conversion, similarly to the findings reported in [4], where the authors exploited Fabry-Pérot resonance in a medium with periodically distributed elliptical holes. REFERENCES [1] G. Bonnet and V. Monchiet. Negative refraction of elastic waves on a metamaterial with anisotropic local resonance. Journal of the Mechanics and Physics of Solids 169, 2022. [2] G. Ma, C. Fu, G. Wang, P. Del Hougne, J. Christensen, Y. Lai and P. Sheng. Polarization bandgaps and fluid-like elasticity in fully solid elastic metamaterials. Nature Communications 7, 2016. [3] D. Faraci, F. Mendicino, A. Vincenti and C. Comi. Wave polarization control in anisotropic locally resonant materials. Applied Sciences 13, 2023. [4] J.M. Kweun, H.J. Lee, J.H. Oh, H.M. Seung and Y.Y. Kim. Transmodal Fabry-Pérot resonance: theory and realization with elastic metamaterials. Phys. Rev. Lett. 118, 2017.
