Modal analysis of bandgap formation for vibration attenuation in locally resonant finite beams

Christopher Sugino, Stephen Leadenham, Massimo Ruzzene, Alper Erturk

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Metamaterials made from locally resonating arrays can exhibit attenuation bandgaps at wavelengths much longer than the lattice size, enabling low-frequency vibration attenuation. For an effective use of such locally resonant metamaterial concepts, it is required to bridge the gap between the dispersion characteristics and modal behavior of the host structure with its resonators. To this end, we develop a novel argument for bandgap formation in finite-length beams, relying on modal analysis and the assumption of infinitely many resonators. This assumption is analogous to the wave assumption of an infinitely long beam composed of unit cells, but gives additional analytical insight into the bandgap, and yields a simple formula for the frequency range of the bandgap. We present a design guideline to place the bandgap for a finite beam with arbitrary boundary conditions in a desired frequency range that depends only on the total mass ratio and natural frequency of the resonators. For a beam with a finite number of resonators and specified boundary conditions, we suggest a method for choosing the optimal number of resonators. We validate the model with both finite-element simulations and a simple experiment, and draw conclusions.

Original languageEnglish
Title of host publication28th Conference on Mechanical Vibration and Noise
ISBN (Electronic)9780791850206
DOIs
StatePublished - 2016
EventASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016 - Charlotte, United States
Duration: 21 Aug 201624 Aug 2016

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume8

Conference

ConferenceASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016
Country/TerritoryUnited States
CityCharlotte
Period21/08/1624/08/16

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