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Topological bands and localized vibration modes in quasiperiodic beams | | Raj Kumar Pal
; Matheus I. N. Rosa
; Massimo Ruzzene
; | | Date: |
1 Jun 2019 | | 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. | | Source: | arXiv, 1906.0151 | | Services: | Forum | Review | PDF | Favorites | |
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