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Article Dans Une Revue International Journal of Non-Linear Mechanics Année : 2022

Neimark Sacker bifurcations and non-linear energy exchange in chains of non-linear oscillators

Résumé

We treat a chain of oscillators with linear stiffness and internal and external cubic non-linearities. The method of harmonic balance is used to determine the non-linear modes of the Hamiltonian system. For each equilibrium point, a stability analysis is performed by means of the associated monodromy matrix. The numerical results shows that branch points, limit points and Neimark-Sacker bifurcations exist in the system. The aim of the paper is to study how they drive the energy in the system: branch points make energy transfer between non-linear modes possible, while Neimark-Sacker bifurcations can lead to chaotic behaviour. As the number of oscillators increases, the energy required to reach the first Neimark-Sacker bifurcation follows a remarkable regularity.
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Dates et versions

hal-03659355 , version 1 (04-05-2022)

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Gabriel Hurel, Sébastien Baguet, Claude-Henri Lamarque. Neimark Sacker bifurcations and non-linear energy exchange in chains of non-linear oscillators. International Journal of Non-Linear Mechanics, 2022, 144, pp.104057. ⟨10.1016/j.ijnonlinmec.2022.104057⟩. ⟨hal-03659355⟩
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