Localized Breathing Modes in Granular Crystals with Defects

Details Localized Breathing Modes in Granular Crystals with Defects Localized Breathing Modes in Granular Crystals with Defects

2009-06-22

arxiv.org/abs/0906.4094v1

Phys. Rev. E 80, 066601 (2009)

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

10.1103/PhysRevE.80.066601

We investigate nonlinear localized modes at light-mass impurities in a one-dimensional, strongly-compressed chain of beads under Hertzian contacts. Focusing on the case of one or two such "defects", we analyze the problem's linear limit to identify the system eigenfrequencies and the linear defect modes. We then examine the bifurcation of nonlinear defect modes from their linear counterparts and study their linear stability in detail. We identify intriguing differences between the case of impurities in contact and ones that are not in contact. We find that the former bears similarities to the single defect case, whereas the latter features symmetry-breaking bifurcations with interesting static and dynamic implications.

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