Contact-based and spheroidal vibrational modes of a hexagonal monolayer of microspheres on a substrate
Name
Nelson_Contact-based and spheroidal.pdf
Description
Submitted version
Size
414.95 KB
Format
Adobe PDF
Checksum (MD5)
057cbadc464b8d6745b59fc6c35041c2
Author(s)
Vega-Flick, A
Duncan, RA
Wallen, SP
Boechler, N
Stelling, C
Retsch, M
Alvarado-Gil, JJ
Nelson, KA
Maznev, AA
Date Issued
2018
Journal
Wave Motion
Publisher
Elsevier BV
Version
Original manuscript
Abstract
© 2017 Elsevier B.V. We analytically study acoustic modes of a close-packed hexagonal lattice of spheres adhered to a substrate, propagating along a high-symmetry direction. The model, accounting for both normal and shear coupling between the spheres and between the spheres and the substrate, yields three contact-based vibrational modes involving both translational and rotational motion of the spheres. In addition to contact-based modes, we also study the effect of sphere–substrate and sphere–sphere contacts on spheroidal vibrational modes of the spheres using a perturbative approach. The sphere–substrate interaction results in a frequency upshift for the modes having a non-zero displacement at the contact point with the substrate as well as mode-splitting for some of the degenerate modes of the free sphere. Sphere–sphere interactions result in dispersion of spheroidal modes. Analytical dispersion relations for both contact-based and spheroidal modes are presented and compared with results obtained for a square lattice.
MIT Department
Massachusetts Institute of Technology. Department of Chemistry
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.wavemoti.2017.10.010
