Platonic crystal

Applications

The types of platonic structures that have been examined include arrays of perforations, arrays of pins, arrays of point masses, as well as periodic variations in the plate material itself. Platonic crystals have been shown to exhibit a number of behaviours similar to photonic crystals, including negative refraction, beam splitting, and wave trapping. They may also feature large stopbands where wave propagation is not possible through the crystal, as well as cloaking near degenerate band surfaces. Investigations into defective platonic crystals has also revealed strong energy localization effects within the defects, with high quality factors.

Experimental work in platonics to date has shown promising results in cloaking and flat lens focusing of flexural wave energy.

References

References

1. (2007). "Bloch-Floquet bending waves in perforated thin plates". [[Proceedings of the Royal Society A]].
2. (July 2024). "Focussing bending waves via negative refraction in perforated thin plates". Applied Physics Letters.
3. (2010). "High directivity and confinement of flexural waves through ultra-refraction in thin perforated plates". EPL.
4. (2007). "Penetration of flexural waves through a periodically constrained thin elastic plate in vacuo and floating on water". Journal of Engineering Mathematics.
5. (2009). "Wave scattering by platonic grating stacks". [[Proceedings of the Royal Society A]].
6. (2011). "Fast and slow interaction of elastic waves with platonic clusters". [[Proceedings of the Royal Society A]].
7. (2012). "Transmission, trapping and filtering of waves in periodically constrained elastic plates". [[Proceedings of the Royal Society A]].
8. (2012). "Negative refraction and dispersion phenomena in platonic clusters". [[Waves in Random and Complex Media]].
9. (2012). "Analytic theory of defects in periodically structured elastic plates". [[Proceedings of the Royal Society A]].
10. (2012). "High-frequency asymptotics for microstructured thin elastic plates and platonics". [[Proceedings of the Royal Society A]].
11. (2013). "Moulding flexural waves in elastic plates lying atop a Faqir's bed of nails".
12. (2009). "Platonic crystals: Bloch bands, neutrality and defects". Mechanics of Materials.
13. (2012). "The effect on bending waves by defects in pinned elastic plates". Journal of Sound and Vibration.
14. (2012). "Experiments on elastic cloaking in thin plates". Physical Review Letters.
15. (2013). "Flat lens for time-domain focusing of elastic waves in thin plates". Applied Physics Letters.