Dynamic characteristics of a periodically forced periodic system with a clearance in low frequency vibration

A two-degree-of-freedom periodically forced system with a clearance is considered. Pattern types, diversity, regularity and bifurcation characteristics of the fundamental group of impact vibrations and subharmonic impact vibrations in the parameter plane, under low frequency vibration, are analyzed. The transition irreversibility of adjacent impact vibrations with fundamental period and two types of transition regions (narrow hysteresis and tongues-shaped regions), and a series of singular points are found by multi-target and multi-parameter co-simulation analysis. The occurrence mechanism and distribution characteristics of the hysteresis and tongue-shaped regions, as well as pattern types and regularity of subharmonic impact vibrations in the tongue-shaped regions are studied. The transition law from impact vibrations with fundamental period to incomplete and complete chattering-impact vibrations is studied. (paper)