Journal
ACTA MECHANICA SINICA
Volume 28, Issue 4, Pages 1143-1153Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10409-012-0092-9
Keywords
Phononic crystal; Band structure; Cylindrical wave expansion; Dirichlet-to-Neumann (DtN) map; Bloch theorem
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Funding
- National Natural Science Foundation of China [51178037, 10632020]
- 973 State Key Development Program for Basic Research of China [2010CB732104]
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In this paper, a method based on the Dirichletto-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann (DtN) map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.
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