Amplitude-dependent edge states and discrete breathers in nonlinear modulated phononic lattices

We investigate the spectral properties of one-dimensional spatially modulated nonlinear phononic lattices, and their evolution as a function of amplitude. In the linear regime, the stiffness modulations define a family of periodic and quasiperiodic lattices whose bandgaps host topological edge state...

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Bibliographic Details
Published in:New journal of physics 2023-10, Vol.25 (10), p.103053
Main Authors: Rosa, Matheus I N, Leamy, Michael J, Ruzzene, Massimo
Format: Article
Language:English
Subjects:
Amplitudes
Breathers
discrete breathers
Eigenvalues
Eigenvectors
Lattice vibration
Lattices
Localization
metamaterials
non-linear
Nonlinearity
Physics
quasiperiodic lattices
topological states
Topology
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Summary:We investigate the spectral properties of one-dimensional spatially modulated nonlinear phononic lattices, and their evolution as a function of amplitude. In the linear regime, the stiffness modulations define a family of periodic and quasiperiodic lattices whose bandgaps host topological edge states localized at the boundaries of finite domains. With cubic nonlinearities, we show that edge states whose eigenvalue branch remains within the gap as amplitude increases remain localized, and therefore appear to be robust with respect to amplitude. In contrast, edge states whose corresponding branch approaches the bulk bands experience de-localization transitions. These transitions are predicted through continuation studies on the linear eigenmodes as a function of amplitude, and are confirmed by direct time domain simulations on finite lattices. Through our predictions, we also observe a series of amplitude-induced localization transitions as the bulk modes detach from the nonlinear bulk bands and become discrete breathers that are localized in one or more regions of the domain. Remarkably, the predicted transitions are independent of the size of the finite lattice, and exist for both periodic and quasiperiodic lattices. These results highlight the co-existence of topological edge states and discrete breathers in nonlinear modulated lattices. Their interplay may be exploited for amplitude-induced eigenstate transitions, for the assessment of the robustness of localized states, and as a strategy to induce discrete breathers through amplitude tuning.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/ad016f