Whispering-Bloch elastic circuits

• Published in: Wave motion Vol. 105; p. 102755
• Main Authors: Putley, H.J., Chaplain, G.J., Rakotoarimanga-Andrianjaka, H., Maling, B., Craster, R.V.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-09-2021; Elsevier BV
• Subjects: Arrays; Circuit design; Circuits; Delay lines; Elastic plates; Elasticity; Energy harvesting; Green's functions; Leakage; Materials elasticity; Metamaterial; Platonic; Q factors; Rayleigh–Bloch mode; Resonators; Ring resonator; Simulation; Studies; Wave power; Whispering gallery; Whispering-Bloch mode; Platonic; Ring resonator; Rayleigh–Bloch mode; Whispering gallery; Metamaterial; Whispering-Bloch mode
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2021.102755

We investigate structured arrays and rings in elasticity to design elastic platonic circuits that utilise resonant phenomena. Creating ring resonators, and understanding their coupling to input and output arrays, allows for the development of platonic circuits including add–drop filters (ADFs) and coupled resonator elastic arrays (CREAs), and hence we envisage integrated platonic devices. Structured rings of point-masses placed atop a thin elastic plate lead to highly confined quasi-modes that leak energy; the leakage being quantified by the limiting quality factor Q. The conditions of resonance are deduced using highly accurate numerical simulations based on a Green’s function approach to solve the dispersion relation associated with the structured ring resonators. The sharp resonances that emerge are then used to filter and direct wave energy based on input frequency, and this is illustrated through analogy with devices used in optics, e.g. integrated photonic circuits. The potential applications of the elastic devices include elastic delay lines and passive energy harvesters.
•Periodic structuration of point-masses upon a Kirchhoff–Love plate.•Ring resonators in elasticity exhibit whispering-Bloch resonances.•Elastic ring resonators of exponentially large quality-factor.•Coupled line and ring arrays for manipulation of flexural wave motion.•Elastic Add/Drop Filter provides narrow-band flexural wave filtering.