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Published December 2020 | public
Journal Article

Surface wave non-reciprocity via time-modulated metamaterials


We investigate how Rayleigh waves interact with time-modulated resonators located on the free surface of a semi-infinite elastic medium. We begin by studying the dynamics of a single resonator with time-modulated stiffness, we evaluate the accuracy of an analytical approximation of the resonator response and identify the parameter ranges in which its behavior remains stable. Then, we develop an analytical model to describe the interaction between surface waves and an array of resonators with spatio-temporally modulated stiffness. By combining our analytical models with full-scale numerical simulations, we demonstrate that spatio-temporal stiffness modulation of this elastic metasurface leads to the emergence of non-reciprocal features in the Rayleigh wave spectrum. Specifically, we show how the frequency content of a propagating signal can be filtered and converted when traveling through the modulated medium, and illustrate how surface-to-bulk wave conversion plays a role in these phenomena. Throughout this article, we indicate bounds of modulation parameters for which our theory is reliable, thus providing guidelines for future experimental studies on the topic.

Additional Information

© 2020 Elsevier Ltd. Received 10 August 2020, Revised 7 October 2020, Accepted 7 October 2020, Available online 10 October 2020. AP acknowledges the support of DICAM at the University of Bologna. PC acknowledges the support of the Research Foundation at Stony Brook University. CD acknowledges support from the National Science Foundation under EFRI Grant No. 1741565. The authors wish to thank Lorenz Affentranger and Yifan Wang for useful discussions. CRediT authorship contribution statement: A. Palermo: Conceptualization, Investigation, Formal analysis, Visualization, Writing - original draft. P. Celli: Conceptualization, Investigation, Formal analysis, Visualization, Writing - original draft. B. Yousefzadeh: Conceptualization, Formal analysis, Writing - review & editing. C. Daraio: Conceptualization, Writing - review & editing. A. Marzani: Formal analysis, Resources, Writing - review & editing. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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October 20, 2023