Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

Abstract

A two-degree-of-freedom periodically forced system with a clearance is considered. The correlative relationship and matching law between dynamics and system parameters are analyzed by the co-simulation analysis of multi-parameter and multi-performance. Key parameters of the system, such as the exciting frequency, clearance value and constraint stiffness, are emphasized to analyze the influence of the main factors on its soft impact characteristics and reveal diversity, evolution and distribution regions of periodic-impact motions. The quantity of the fundamental group of \(p/1\) impact motions, which have the excitation period and differ by the number \(p\) of impacts, is basically determined by the constraint stiffness. A series of grazing bifurcations occur with decreasing the exciting frequency so that the number \(p\) of impacts of the fundamental group of motions correspondingly increases one by one. As the constraint stiffness is very large, the impact number \(p\) of the fundamental group of motions becomes also big enough in low exciting frequency range. Consequently, the system possibly exhibits chattering-impact characteristics and the relative impact velocities successively attenuate in an excitation period. There exist a series of singular points between any two adjacent ones of the fundamental group of motions as the damping ratio or the damping constant of the viscous dashpot connecting two masses is very small, i.e., real-grazing and bare-grazing bifurcation boundaries of one of them, saddle-node and period-doubling bifurcation boundaries of the other mutually cross themselves at the point of intersection and create two types of transition regions: hysteresis and tongue-shaped regions. A series of zones of regular and complex subharmonic impact motions are found to dominate in the tongue-shaped regions. The dimensionless parameters have been designed technically, under which large mass ratio or small supporting stiffness ratio leads to diversity and complexity of periodic-impact motions of the system. Based on the sampling ranges of parameters, the influence of system parameters on relative impact velocities, existence regions and correlative distribution of different types of periodic-impact motions of the system is emphatically studied.