25 research outputs found
Asymptotic of 'rigid-body' motions for nonlinear dynamics: physical insight and methodologies
The purpose of the present work is to show that an adequate basis for
understanding the essentially nonlinear phenomena must also be essentially
nonlinear however still simple enough to play the role of a basis. It is shown
that such types of 'elementary' nonlinear models can be revealed by tracking
the hidden links between analytical tools of analyses and subgroups of the
rigid-body motions or, in other terms, rigid Euclidean transformation. While
the subgroup of rotations is linked with linear and weakly nonlinear
vibrations, the translations with reflections can be viewed as a geometrical
core of the strongly nonlinear dynamics associated with the so-called
vibro-impact behaviors. It is shown that the corresponding analytical approach
develops through non-smooth temporal substitutions generated by the impact
models.Comment: Presented at 12th DSTA Conference, December 2-5, 2013 {\L}\'od\'z,
Polan
Escape of a harmonically forced particle from an infinite-range potential well: a transient resonance
Periodic motions of coupled impact oscillators
International audienceWe study the existence and stability of time-periodic oscillations in a chain of coupled impact oscillators, for rigid impacts without energy dissipation. We formulate the search of periodic solutions as a boundary value problem incorporating unilateral constraints. This problem is solved analytically in the vicinity of the uncoupled limit and numerically for larger coupling constants. Different solution branches corresponding to nonlinear localized modes (breathers) and normal modes are computed