Periodic Vibration and Bifurcation of Vibratory Systems with Clearance Composed of Rigid Constraints

Abstract

Abstract A periodically-forced vibratory system with clearance composed of bilateral symmetric rigid constraints is considered. Distribution characteristics and bifurcation boundaries of various periodic-impact vibraitons of the vibratory system are analyzed and specified. The transition process between neighbouring fundamental impact vibrations is discussed. The induced mechanism of the two kinds of transition domains, such as hysteresis and tongue-shaped domains, and a series of singularities are revealed. Analysis results show that on the basis of the initial conditions of the system vibration or the change of excitation frequency or clearance, neighbouring fundamental impact vibrations can coexist in the hysteresis domain. Meanwhile, there exists a series of sub-harmonic impact vibrations in the tongue-shaped domain. These multi-period and multi-impact vibrations usually undergo period doubling or grazing bifurcation along with the change of excitation frequency or clearance.