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Using the Mass Ratio to Induce Band Gaps in a 1D Array of Nonlinearly Coupled Oscillators

[+] Author Affiliations
Brian P. Bernard, Jeffrey W. Peyser, Brian P. Mann

Duke University, Durham, NC

David P. Arnold

University of Florida, Gainesville, FL

Paper No. DETC2012-70403, pp. 1155-1159; 5 pages
  • ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 24th Conference on Mechanical Vibration and Noise, Parts A and B
  • Chicago, Illinois, USA, August 12–15, 2012
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4500-4
  • Copyright © 2012 by ASME


A one dimensional system of nonlinearly coupled magnetic oscillators has been studied. After deriving the equations of motion for each oscillator, the system is linearized about a stable equilibrium and studied using an assumed solution form for a traveling wave. Wave propagation and attenuation regions are predicted by reducing the system of equations to a standard eigenvalue problem. Through evaluating these equations across the entire irreducible Brillouin zone, it is determined that when the masses of each oscillator are identical, the entire frequency range of the system is a propagation zone. By varying the masses comprising a unit cell, band gaps are observed. It is shown that the mass ratio can be used to guide both the size and location of these band gaps. Numerical simulations are performed to support our analytical findings.

Copyright © 2012 by ASME
Topics: Energy gap



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