Discontinuous dynamics of a 3-DOF oblique-impact system with dry friction and single pendulum device

Abstract

Based on the high-dimensional flow switchability theory in discontinuous dynamical systems, this paper aims at investigating the dynamical behaviors of a 3-DOF (three degree-of-freedom) oblique-impact system with dry friction and single pendulum device. The oblique impact system considered in this paper consists of elastic contact model and Coulomb friction model; meanwhile, the unequal kinetic and static friction coefficients result in the flow barriers. Firstly, according to two factors that cause discontinuity, namely friction and impact, different regions, boundaries and edges are delineated in four- and two-dimensional phase spaces. Secondly, the conditions of motion transformation at separation boundaries are developed. Thirdly, the switching criteria of motion at the edges in four-dimensional phase space are deduced, which is a further extension and enrichment of flow switching theory in higher-dimensional space. Finally, some typical motions are visually demonstrated by numerical simulations, and the sliding bifurcation scenarios are presented. Compared with low-dimensional flow switchability theory, this method can more systematically study the dynamic behaviors of multiple degree-of-freedom system under the simultaneous action of multiple objects and give more convenient analytical conditions. The study on the complex motion mechanism of such a 3-DOF oblique-impact system provides a reference for the parameter selection of single pendulum shock absorbers, which is useful in exploring how to suppress the vibration/noise of friction/impact system in mechanical engineering field.