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.
Skip Nav Destination
ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 12–15, 2012
Chicago, Illinois, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-4500-4
PROCEEDINGS PAPER
Using the Mass Ratio to Induce Band Gaps in a 1D Array of Nonlinearly Coupled Oscillators
Brian P. Bernard,
Brian P. Bernard
Duke University, Durham, NC
Search for other works by this author on:
Jeffrey W. Peyser,
Jeffrey W. Peyser
Duke University, Durham, NC
Search for other works by this author on:
David P. Arnold
David P. Arnold
University of Florida, Gainesville, FL
Search for other works by this author on:
Brian P. Bernard
Duke University, Durham, NC
Jeffrey W. Peyser
Duke University, Durham, NC
Brian P. Mann
Duke University, Durham, NC
David P. Arnold
University of Florida, Gainesville, FL
Paper No:
DETC2012-70403, pp. 1155-1159; 5 pages
Published Online:
September 9, 2013
Citation
Bernard, BP, Peyser, JW, Mann, BP, & Arnold, DP. "Using the Mass Ratio to Induce Band Gaps in a 1D Array of Nonlinearly Coupled Oscillators." Proceedings of the 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. pp. 1155-1159. ASME. https://doi.org/10.1115/DETC2012-70403
Download citation file:
5
Views
Related Proceedings Papers
One Way Sound Propagation in a Smart Fluid
SMASIS2017
Related Articles
Band Gap Formation and Tunability in Stretchable Serpentine Interconnects
J. Appl. Mech (September,2017)
Wave Motion in Periodic Flexural Beams and Characterization of the Transition Between Bragg Scattering and Local Resonance
J. Appl. Mech (January,2012)
Tuning Band Structures of Two-Dimensional Phononic Crystals With Biasing Fields
J. Appl. Mech (September,2014)
Related Chapters
A High Resolution DOA Estimation Method Based on Maximal Eigenvector Reconstruction
International Conference on Future Computer and Communication, 3rd (ICFCC 2011)
Research on the Adaptation of Strength Reduction Method Using FLAC
Geological Engineering: Proceedings of the 1 st International Conference (ICGE 2007)
Electronic Properties of a Two-Dimensional Ring-Shaped Kronig-Penney Lattice with a Positional Disorder
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3