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Localized breathing modes in granular crystals with defects.

G Theocharis¹, M Kavousanakis, P G Kevrekidis

¹Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 7, 2010

Summary

This summary is machine-generated.

Light-mass impurities are essential for creating localized modes in compressed elastic chains. Nonlinearity causes frequency-dependent amplitudes and symmetry-breaking, crucial for understanding wave propagation in these systems.

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Area of Science:

Nonlinear dynamics
Condensed matter physics
Mechanical metamaterials

Background:

One-dimensional elastic chains exhibit complex behaviors under compression.
Intrinsic nonlinearity from Hertzian contact interactions is a key feature.
Localized modes are essential for energy confinement and wave manipulation.

Purpose of the Study:

Investigate the emergence of localized modes in compressed elastic chains with impurities.
Analyze the role of nonlinearity and impurity presence in mode formation.
Characterize the stability and behavior of these localized modes.

Main Methods:

Analysis of the linear limit to identify eigenfrequencies and linear defect modes.
Application of continuation techniques to find nonlinear solutions.
Detailed linear stability analysis of the obtained solutions.

Main Results:

Nonlinearity alone does not support localized, breathing modes in uniform chains.
Light-mass impurities are crucial for the appearance of localized modes.
Nonlinearity induces frequency-dependent oscillation amplitudes and static displacements.
Symmetry-breaking bifurcations occur in chains with two non-contacting defects.

Conclusions:

Localized modes in compressed elastic chains are critically dependent on light-mass impurities.
Nonlinearity introduces complex phenomena such as amplitude-frequency dependence and symmetry breaking.
These findings are vital for designing materials with tailored wave propagation properties.