97 research outputs found
Small-World Disordered Lattices: Spectral Gaps and Diffusive Transport
We investigate the dynamic behavior of lattices with disorder introduced
through non-local network connections. Inspired by the Watts-Strogatz
small-world model, we employ a single parameter to determine the probability of
local connections being re-wired, and to induce transitions between regular and
disordered lattices. These connections are added as non-local springs to
underlying periodic one-dimensional (1D) and two-dimensional (2D) square,
triangular and hexagonal lattices. Eigenmode computations illustrate the
emergence of spectral gaps in various representative lattices for increasing
degrees of disorder. These gaps manifest themselves as frequency ranges where
the modal density goes to zero, or that are populated only by localized modes.
In both cases, we observe low transmission levels of vibrations across the
lattice. Overall, we find that these gaps are more pronounced for lattice
topologies with lower connectivity, such as the 1D lattice or the 2D hexagonal
lattice. We then illustrate that the disordered lattices undergo transitions
from ballistic to super-diffusive or diffusive transport for increasing levels
of disorder. These properties, illustrated through numerical simulations,
unveil the potential for disorder in the form of non-local connections to
enable additional functionalities for metamaterials. These include the
occurrence of disorder-induced spectral gaps, which is relevant to frequency
filtering devices, as well as the possibility to induce diffusive-type
transport which does not occur in regular periodic materials, and that may find
applications in dynamic stress mitigation
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