Stochastic variational inequalities for elasto-plastic oscillators
Alain Bensoussan, Jànos Turi · Comptes Rendus Mathématique · 2006
The purpose of this Note is to show that models used in the literature for the hysteresis effect of non-linear elasto-plastic oscillators submitted to random vibrations are equivalent to stochastic variational inequalities. This powerful tool allows to study the ergodic properties of the Markov process related to the displacement. We characterize completely the invariant measure by a partially degenerate elliptic partial differential equation, with new Dirichlet coupling conditions.