Contact-based and spheroidal vibrational modes of a hexagonal monolayer of microspheres on a substrate
© 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...
| Main Authors: | , , , , , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Elsevier BV
2021
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| Online Access: | https://hdl.handle.net/1721.1/133450 |
| Summary: | © 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. |
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