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Here we report the results obtained for band structure calculations of phononic crystals with rigid scatterers using the plane-wave expansion method. A scatterer with infinite acoustic impedance is modeled by approaching either the mass density or the elastic modulus to infinity. It is shown, that in both cases the dispersion equation contains singular matrices. This singularity leads to the correct band structure in the case of infinite elastic modulus. However, in the limiting case of infinite density the dispersion equation becomes meaningless. We explain the mathematical reason for this drastic difference.
Dmitrii Shymkiv andArkadii Krokhin
"Mathematical singularity in the band structure calculations for phononic crystal with rigid scatterers (Conference Presentation)", Proc. SPIE 12488, Health Monitoring of Structural and Biological Systems XVII, 1248811 (12 June 2023); https://doi.org/10.1117/12.2658509
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Dmitrii Shymkiv, Arkadii Krokhin, "Mathematical singularity in the band structure calculations for phononic crystal with rigid scatterers (Conference Presentation)," Proc. SPIE 12488, Health Monitoring of Structural and Biological Systems XVII, 1248811 (12 June 2023); https://doi.org/10.1117/12.2658509