Publication Date:
2015-12-24
Description:
Publication date: March 2016 Source: Wave Motion, Volume 61 Author(s): Young Kwan Ahn, Joo Hwan Oh, Pyung Sik Ma, Yoon Young Kim The supercell approach can be useful for tailoring dispersion curves of phononic crystals, but the interpretation of the dispersion curves in the supercells can be often intriguing. Supercells formed by integer multiples of an original unit cell along its lattice axes are common, but there are also important situations requiring supercells formed by non-integer multiples of an original unit cell and its rotation with respect to its lattice axes. In these cases, not only dispersion branch folding, but also branch overlapping not found in common supercells, take place, which complicates the correct interpretation of band structures. In this study, we consider 45°-rotated augmented supercells and analyze why and how branch folding and overlapping take place. For the analysis, the relation between the first Brillouin zone of an original cell and that of the corresponding 45°-rotated augmented supercell is investigated. The analysis of the folding and overlapping mechanism found in the dispersion curve of the supercell is also useful for interpreting which branches can be excited over a target wavevector direction. The usefulness of the findings of this supercell-based dispersion analysis is demonstrated in unit cell design problems. Specifically, we show how to interpret correctly the dispersion curves of phononic crystals made of unit cells optimized by bandgap maximizing topology optimization when the optimized unit cells turn out to be 45°-rotated augmented supercells. Conversely, throughout design optimization iterations, the original period of a unit cell that is initially set at the beginning of design optimization can be maintained if branch overlapping is forced not to occur.
Print ISSN:
0165-2125
Electronic ISSN:
1878-433X
Topics:
Geosciences
,
Physics
Permalink
