Abstract
The propagation of elastic or acoustic waves in phononic crystals can be described via wave equations with periodically varying coefficients. In this chapter, we give an overview of different methods that have been used to compute phononic band structures and transmission through phononic crystals, and investigate the properties of phononic crystal waveguides and cavities. We first present general considerations on the equations and the types of problems that have been considered. We then introduce four different methods: (layer) multiple scattering theory, plane wave expansion, finite-difference time-domain, and finite element methods. Rather than giving a full account of each method, we stress their generic properties, capacities, and limitations. We hope this discussion will be useful for the reader to decide which method to select for a specific problem.
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Notes
- 1.
A supercell extends a few periods away from the defect it encloses. Modal computations then give physically meaningful results when only evanescent Bloch waves of the elementary phononic crystal exist, i.e., inside a complete band gap. Furthermore, the number of phononic crystal rows must be sufficient so that the Bloch wave with the least imaginary part of the wave vector can be considered negligible on the boundary of the supercell.
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Laude, V., Khelif, A. (2016). Computational Problems and Numerical Techniques for the Analysis of Phononic Crystals. In: Khelif, A., Adibi, A. (eds) Phononic Crystals. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9393-8_4
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