Dynamics of SDOF oscillators with hysteretic motion-limiting stop.

Interest in impact vibrations is two-fold: (i) a wide range ofpractical problems involve bodies colliding with one another or/and with obstacles, and (ii) the complex dynamics of such problems is a good testing bench for nonlinear theories. The assumption of rigid stop isquite popular, although unfortunately it does not allow us to simulate the actual dissipative character of the impact response, but via apriori fixed coefficient of restitution. However, the correct description of the energy dissipated during impact is very important. In this paper, the dynamic response of a single-degree-of-freedoms ystem is studied, where hysteretic stop, which allows the simulation ofthe real behaviour of a wide range of material pairings, is assumed; a distinction between hard and soft contacts is made according to theimpulsive or non impulsive nature of the contact reaction. 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 placeand the obstacle. For different clearances, strange attractors are revealed and their evolution illustrated. Furthermore, in the case of hard contact, an equivalent coefficient of restitution is proposed which depends, in a simple way, on some characteristic parameters of the hysteretic contact law. Such a coefficient, not given a priori but obtained via simulation of physical behaviour, provides the definition of an equivalent impact oscillator (i.e. with rigid stop).