The forced dynamics of chains of linearly coupled mechanical oscillators characterized by on-site cubic nonlinearity is investigated. The study aims to highlight the role played by the harmonic excitation on the nonlinear spatially localised dynamics of the system. Towards this goal, a map approach is employed in order to identify the chain nonlinear propagation regions under 1:1 resonance conditions. Given the latter assumption, the governing second-order difference equation refers to a perturbation of the stationary resonant response. Softening and hardening type of nonlinearities are considered and the associated unstaggered and staggered discrete breathers (DB), respectively, are discussed. Stationary DBs obtained as soliton-like solutions are identified either with sequences of the nonlinear map homoclinic primary intersection points and with an ad hoc analytic approximation; the latter is based on the idea that the nonlinearity is taken into account only in the central part of the breather whilst the tails are treated as linear excitations.

Discrete breathers in forced chains of oscillators with cubic nonlinearities / Romeo, Francesco; Gendelman, Oleg V.. - 19:(2016), pp. 236-243. (Intervento presentato al convegno IUTAM Symposium Analytical Methods in Nonlinear Dynamics tenutosi a Francoforte) [10.1016/j.piutam.2016.03.030].

Discrete breathers in forced chains of oscillators with cubic nonlinearities

ROMEO, Francesco
Primo
;
2016

Abstract

The forced dynamics of chains of linearly coupled mechanical oscillators characterized by on-site cubic nonlinearity is investigated. The study aims to highlight the role played by the harmonic excitation on the nonlinear spatially localised dynamics of the system. Towards this goal, a map approach is employed in order to identify the chain nonlinear propagation regions under 1:1 resonance conditions. Given the latter assumption, the governing second-order difference equation refers to a perturbation of the stationary resonant response. Softening and hardening type of nonlinearities are considered and the associated unstaggered and staggered discrete breathers (DB), respectively, are discussed. Stationary DBs obtained as soliton-like solutions are identified either with sequences of the nonlinear map homoclinic primary intersection points and with an ad hoc analytic approximation; the latter is based on the idea that the nonlinearity is taken into account only in the central part of the breather whilst the tails are treated as linear excitations.
2016
IUTAM Symposium Analytical Methods in Nonlinear Dynamics
lattices , Solitons, intrinsic localized
04 Pubblicazione in atti di convegno::04b Atto di convegno in volume
Discrete breathers in forced chains of oscillators with cubic nonlinearities / Romeo, Francesco; Gendelman, Oleg V.. - 19:(2016), pp. 236-243. (Intervento presentato al convegno IUTAM Symposium Analytical Methods in Nonlinear Dynamics tenutosi a Francoforte) [10.1016/j.piutam.2016.03.030].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/872115
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