Amplitude-dependent topological edge states in nonlinear phononic lattices

Physical Review. E
Raj Kumar PalMassimo Ruzzene

Abstract

This work investigates the effect of nonlinearities on topologically protected edge states in one- and two-dimensional phononic lattices. We first show that localized modes arise at the interface between two spring-mass chains that are inverted copies of each other. Explicit expressions derived for the frequencies of the localized modes guide the study of the effect of cubic nonlinearities on the resonant characteristics of the interface, which are shown to be described by a Duffing-like equation. Nonlinearities produce amplitude-dependent frequency shifts, which in the case of a softening nonlinearity cause the localized mode to migrate to the bulk spectrum. The case of a hexagonal lattice implementing a phononic analog of a crystal exhibiting the quantum spin Hall effect is also investigated in the presence of weakly nonlinear cubic springs. An asymptotic analysis provides estimates of the amplitude dependence of the localized modes, while numerical simulations illustrate how the lattice response transitions from bulk-to-edge mode-dominated by varying the excitation amplitude. In contrast with the interface mode of the first example studies, this occurs both for hardening and softening springs. The results of this study provi...Continue Reading

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Citations

Nov 6, 2018·Physical Review Letters·D A DobrykhYu S Kivshar
Oct 20, 2018·Proceedings. Mathematical, Physical, and Engineering Sciences·M I Hussein, R Khajehtourian
Aug 7, 2019·Physical Review Letters·Matheus I N RosaMassimo Ruzzene
Oct 24, 2019·Physical Review. E·Matthew D Fronk, Michael J Leamy
Feb 20, 2021·Physical Review. E·Weijian Jiao, Stefano Gonella
Apr 15, 2021·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Thomas Benjamin SmithAlessandro Principi
Sep 20, 2019·The Journal of Physical Chemistry Letters·José D Cojal GonzálezJürgen P Rabe

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