Breathers in periodic granular chains with multiple band gaps

摘要

We consider the localized nonlinear breathing modes that emerge in heterogeneous granular configurations ofntwo materials with a periodicity of three and four beads. We examine as characteristic examples chains with onensteel and two aluminum beads, as well as ones with one steel and three aluminum beads, although we brieflyntouch upon other configurations as well, illustrating their similar characteristics.We analyze the higher order gapsnthat emerge in such settings and explore the intrinsic localized modes that bifurcate from the edge of the uppernbands. A generic surprising feature of such states is that they appear to be more robust than their counterpartsnbifurcating from the edges of the lower bands. Direct numerical simulations, using driving of the system atnsuitable frequencies through an actuator or taking advantage of the modulational instabilities of extended bandnedge states in the system, illustrate the spontaneous formation of localized modes within the correspondingnnearest gaps. In these numerical experiments, we also account for the presence of dissipation and analyze itsnpotential role.