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Published September 2019 | Published + Submitted
Journal Article Open

Topological bands and localized vibration modes in quasiperiodic beams

Abstract

We investigate a family of quasiperiodic continuous elastic beams, the topological properties of their vibrational spectra, and their relation to the existence of localized modes. We specifically consider beams featuring arrays of ground springs at locations determined by projecting from a circle onto an underlying periodic system. A family of periodic and quasiperiodic structures is obtained by smoothly varying a parameter defining such projection. Numerical simulations show the existence of vibration modes that first localize at a boundary, and then migrate into the bulk as the projection parameter is varied. Explicit expressions predicting the change in the density of states of the bulk define topological invariants that quantify the number of modes spanning a gap of a finite structure. We further demonstrate how modulating the phase of the ground springs distribution causes the topological states to undergo an edge-to-edge transition. The considered configurations and topological studies provide a framework for inducing localized modes in continuous elastic structural components through globally spanning, deterministic perturbations of periodic patterns defined by the considered projection operations.

Additional Information

© 2019 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 27 May 2019; Accepted 20 August 2019; Accepted Manuscript online 20 August 2019; Published 10 September 2019. The authors gratefully acknowledge funding support from the National Science Foundation through the CMMI 1719728 and EFRI 1741685 grants.

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Published - Pal_2019_New_J._Phys._21_093017.pdf

Submitted - 1906.00151.pdf

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Created:
August 19, 2023
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October 18, 2023