Forced motion of friction oscillators limited by a rigid or deformable obstacle.

The forced dynamics of nonsmooth oscillators have not yet been sufficiently investigated when damping is simultaneously due to friction and impact. Because of the theoretical and practical interest in this type of system, an effort is made in this article to determine the behavior of a single-degree-of-freedom oscillator colliding with an obstacle and excited by a harmonic driving force and by a moving base with constant velocity. The response of this system has been investigated under the assumptions of rigid stop and of Coulomb's friction law, with a static coefficient of friction included that is different from the kinetic one. The evolution through stable closed orbits and period-doubling routes to chaos are studied in terms of the clearance between the mass in the initial place and the obstacle. Periodic solutions exhibiting more than one stop and more than one collision per cycle as well as chaotic motions are investigated. An improvement of the friction-impact model is proposed that allows simulating an exponential velocity-dependent friction law and a deformable (hysteretic) obstacle. This model was tested via a sample application