Intrinsic Energy Localization Through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals
Abstract
We study localized modes in uniform one-dimensional chains of tightly packed and uniaxially compressed elastic beads in the presence of one or two light-mass impurities. For chains composed of beads of the same type, the intrinsic nonlinearity, which is caused by the Hertzian interaction of the beads, appears not to support localized, breathing modes. Consequently, the inclusion of light-mass impurities is crucial for their appearance. By analyzing the problem's linear limit, we identify the system's eigenfrequencies and the linear defect modes. Using continuation techniques, we find the solutions that bifurcate from their linear counterparts and study their linear stability in detail. We observe that the nonlinearity leads to a frequency dependence in the amplitude of the oscillations, a static mutual displacement of the parts of the chain separated by a defect, and for chains with two defects that are not in contact, it induces symmetry-breaking bifurcations.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 2010
- Accession Number
- ADA559097
Entities
People
- C. Daraio
- G. Theocharis
- Mason Porter
- Nicholas Boechler
- P. Kevrekidis
- S. Job
Organizations
- California Institute of Technology