On discontinuous dynamical behaviors of a 2-DOF impact oscillator with friction and a periodically forced excitation

Abstract

In this paper, a 2-DOF (two-degree-of-freedom) impact oscillator with friction and a periodically forced excitation is investigated via using the flow switchability theory in discontinuous dynamical systems. Based on the discontinuities caused by friction and impact between the two masses, the phase space is partitioned into different boundaries and domains. Using the G-functions and vector fields, the analytical conditions of grazing motions and passable motions are discussed, and the appearing and vanishing conditions of sliding motions and side-stick motions are also developed. The periodic motions with stick or non-stick are described through the generic mappings. For better understanding of the analytical conditions of periodic motions, grazing motions, stick motions and passable motions, the velocity and displacement time-histories, G-function responses and trajectories are presented. The investigation on such a 2-DOF impact oscillator with friction may be helpful for achieving optimal design of the single row cylindrical roller bearing systems. Besides, it has an important significance to the noise suppression in mechanical systems with clearance.