title: Local resonance bandgaps in periodic media: theory and experiment.
abstract: Periodic composites such as acoustic metamaterials use local resonance phenomenon in designing low frequency sub-Bragg bandgaps. These bandgaps emerge from a resonant scattering interaction between a propagating wave and periodically arranged resonators. This paper develops a receptance coupling technique to combine the dynamics of the resonator with the unit cell dynamics of the background medium to analyze flexural wave transmission in a periodic structure, involving a single degree of freedom coupling between the medium and the resonator. Receptance techniques allow for a straightforward extension to higher dimensional systems with multiple degrees of freedom coupling and for easier experimental measurements. Closed-form expressions for the location and width of sub-Bragg bandgaps are obtained. Rigid body modes of the unit cell of the background medium are shown to set the bounding frequencies for local resonance bandgaps. Results from the receptance analysis compare well with Bloch wave analysis and experiments performed on a finite structural beam with periodic masses and resonators. Stronger coupling and inertia of the resonator increase the local resonance bandgap width. Two-fold periodicity widens the Bragg bandgap, narrowed by local resonators, thus expanding the design space and highlighting the advantages of hierarchical periodicity.
authors: Department of Mechanical Engineering, The University of British Columbia, 6250 Applied Science Lane, Vancouver, BC V6T1Z4 Canada.
authors: L
authors: L
authors: Raghavan
authors: A Srikantha
authors: AS
authors: Phani
mesh_terms: D000162:Acoustics / Q000295:instrumentation; D003198:Computer Simulation; D004548:Elasticity; D004867:Equipment Design; D008962:Models, Theoretical; D009038:Motion; D009716:Numerical Analysis, Computer-Assisted; D010507:Periodicity; D013016:Sound; D013997:Time Factors; D014732:Vibration