Exact solutions for discrete breathers in forced-damped chain

Abstract

Exact solutions for symmetric discrete breathers (DBs) are obtained in forced-damped linear chain with on-site vibro-impact constraints. The damping is related to inelastic impacts; the forcing may be chosen from broad class of periodic antisymmetric functions. Global conditions for existence and stability of the DB are established. Some unusual phenomena, like non-monotonous dependence of the stability boundary on the forcing amplitude, are revealed analytically for the full system and illustrated numerically for small periodic lattices.

13 pages, 10 figures

References in corpus (3)

• Discrete breathers in a forced-damped array of coupled pendula: Modeling, Computation and Experiment
• Intrinsic localized modes in parametrically-driven arrays of nonlinear resonators
• Experimental observation of the bifurcation dynamics of an intrinsic localized mode in a driven 1-D nonlinear lattice

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• Flat bands and compactons in mechanical lattices
• Front propagation in lattices with on-site bistable non-degenerate potential: multiplicity, bifurcations and route to chaos
• Transient dynamics in strongly nonlinear systems: optimization of initial conditions on the resonant manifold
• Localization in finite asymmetric vibro-impact chains
• Localization in Coupled Finite Vibro-Impact Chains: Discrete Breathers and Multibreathers
• Breather arrest in a chain of damped oscillators with Hertzian contact