Periodic motions of coupled impact oscillators

Vincent Acary 1, * Guillaume James 1, 2 Franck Pérignon 3
* Corresponding author
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : In this work, we study the existence and stability of time-periodic oscillations in a chain of linearly coupled impact oscillators reminiscent of a model analyzed in [2], for rigid impacts without energy dissipation. We introduce a numerical method allowing to compute branches of time-periodic so- lutions when an arbitrary number of nodes undergo rigid impacts. For this purpose, we reformulate the search of periodic solutions as a boundary value problem incorporating unilateral constraints. We illustrate this numerical approach by computing some families of nonlinear spatially localized modes (breathers) and extended modes.
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Vincent Acary, Guillaume James, Franck Pérignon. Periodic motions of coupled impact oscillators. 11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI), Jul 2014, Barcelona, Spain. ⟨hal-01062523⟩

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