Breathers In Periodic Granular Chains With Multiple Band Gaps

TL;DR

This paper investigates localized nonlinear breathing modes in periodic granular chains with multiple band gaps, revealing their robustness and formation mechanisms through numerical simulations.

Contribution

It introduces the analysis of higher order gaps and intrinsic localized modes in heterogeneous granular chains with multiple periodicities, highlighting their robustness.

Findings

Localized modes bifurcate from upper band edges.

Localized modes are more robust than lower band edge counterparts.

Numerical simulations demonstrate spontaneous formation of localized modes.

Abstract

We consider the localized nonlinear breathing modes that emerge in heterogeneous granular configurations of two materials with a periodicity of three and four beads. We examine as characteristic examples chains with 1 steel and 2 alumnium beads, as well as ones with 1 steel and three aluminum beads. We analyze the higher order gaps that emerge in such settings and explore the intrinsic localized modes that bifurcate from the edge of the upper bands. A generic surprising feature of such states is that they appear to be more robust than their counterparts bifurcating from the edges of the lower bands. Direct numerical simulations, using driving of the system at suitable frequencies through an actuator or taking advantage of the modulational instabilities of extended band edge states in the system illustrate the spontaneous formation of localized modes within the corresponding nearest gaps.