Chaotic behaviour of some piecewise-linear systems, part II: Systems with clearance

Chaos and Multiple Periods in an Unsymmetrical Spring and Damping System With Clearance

“…The Feigenbaum number is popular to distinguish this type of route to chaos. The second type of route to chaos, intermittent route to chaos, is demonstrated in literature [7]. The intermittency occurs due to the sudden changes of the size of chaotic attractors, sudden appearances of the chaotic attractors (a possible route to chaos), and sudden destructions of the chaotic attractors and their basin [21,22].…”

“…An extensive discussion is available in literature [7] for the bilinear sti!ness system free in the clearance, and also elastically connected in the clearance. The intermittent route to chaos has been observed mostly in this literature.…”

“…The damping factor has also great e!ect in causing the non-periodic motions on the non-linear system [15]. The clearance problem has been modelled as a single degree of freedom from early literatures [2,4,5,7] to recent ones [3,15,17,18]. Multi-degree-of-freedom model has been carried out recently in some literatures [11,12].…”

Vibro-impacts induced by non-linear resonances in hertzian contacts

“…In several applications, this assumption cannot be justified and it needs to introduce contact stiffness and contact damping. For this end, piecewise linear systems are generally considered [5][6][7][8][9] but few studies are based on a Hertzian contact law and on a non-linear damping law. In the present paper, we propose to consider the fundamental case of a loaded sphere-plane Hertzian contact.…”

Nonlinear regulation of a Lorenz system by feedback linearization techniques

“…These equations, which may have a simple structure, can be used as models for describing unpredictable behavior. Therefore, chaotic models may be useful to understand better many important phenomena [10], [7], [17], [5], [1].…”