While resonant propagation modes are non-existent within band gaps in infinite periodic structures, it is possible for anomalous band-gap resonances to appear in finite periodic structures. We establish two criteria for the characterization of band-gap resonances and propose approaches for their elimination. By considering flexural periodic beams, we show that as the number of unit-cells is increased the vibration response corresponding to band-gap resonances (1) does not shift in frequency, and (2) drops in amplitude. Both these outcomes are not exhibited by regular pass-band resonances, nor by resonances in finite homogenous beams when the length is changed. Our conclusions stem from predictions based on Timoshenko beam theory coupled with matching experimental observations.
Analysis of Periodicity Termination in Phononic Crystals
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Davis, BL, Tomchek, AS, Flores, EA, Liu, L, & Hussein, MI. "Analysis of Periodicity Termination in Phononic Crystals." Proceedings of the ASME 2011 International Mechanical Engineering Congress and Exposition. Volume 8: Mechanics of Solids, Structures and Fluids; Vibration, Acoustics and Wave Propagation. Denver, Colorado, USA. November 11–17, 2011. pp. 973-977. ASME. https://doi.org/10.1115/IMECE2011-65666
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