Bifurcation Characteristics of Fundamental and Subharmonic Impact Motions of a Mechanical Vibration System with Motion Limiting Constraints on a Two-Parameter Plane

Abstract

A two-degree-of-freedom periodically forced system with multiple gaps and rigid constraints is studied. Multiple types of impact vibrations occur at each rigid constraint and interact with each other, which results in the emergence of some complex transitions in the system. Through the cosimulation of the key parameters gap value δ between the two masses and the excitation force frequency ω, the types, existence areas, and bifurcation regularities of the periodic and subharmonic motions can be obtained on the (ω, δ)-parameter plane. In the corresponding three-dimensional surface diagram of the maximum impact velocity, the distribution law of the maximum impact velocity at each constraint can be obtained. The transition laws of fundamental impact motions in the low-frequency parameter domain are studied, and two types of transition regions in the transitions of adjacent fundamental impact motions are found: tongue-like regions and hysteresis regions. Moreover, these two types of transition regions show some atypical partitioning and deformation due to the combined effects of impact vibrations at each constraint. By combining the two-parameter plane diagram and the three-dimensional surface diagram, the effect of changing the gap values between each mass and the fixed constraint and the damping coefficient ζ on the dynamic characteristics of the system is studied. Combining the existence areas of periodic motions and the distribution of maximum impact velocity can provide guidance for the reasonable selection of system parameters.