Motion Analysis of Impact Oscillators with Symmetrical and Asymmetrical Rigid Constraints in Two-Parameter Bifurcation Plane

Abstract

The excited, one-degree-of-freedom mechanical system with symmetrical and asymmetrical rigid constraints, is investigated in a two-parameter bifurcation plane [Formula: see text]–[Formula: see text]. Decision conditions for the chattering-sticking motion of the system are given. The analytical solution of [Formula: see text] periodic motion and the linearization matrix of the Poincaré map are derived. The bifurcation characteristics of the [Formula: see text] periodic motion are analyzed theoretically by the position of the eigenvalue passing through the unit circle. The multiplicity and evolution of periodic motions of the system with symmetrical and asymmetrical constraints are explained by zones of their occurrence and stability in the plane of [Formula: see text]–[Formula: see text]. Special attention is given to the complex dynamics near the singular points [Formula: see text] and the mutual transfer law of adjacent [Formula: see text] motion. The singular point is a codimensional-2 grazing bifurcation point related to [Formula: see text] type, and also a codimensional-2 flip-fold bifurcation point related to [Formula: see text] motion. The mutual evolution of adjacent [Formula: see text] motion is reversible only at the singular point [Formula: see text]. For symmetrical system, motions [Formula: see text], [Formula: see text], [Formula: see text] and their evolutions emerge in the ligulate zone. For an asymmetrical system, a cluster of abnormal basic groups gathers in the low-frequency. The symmetrical constraint model is a special case of the asymmetrical model. The obtained results have reference value for reducing component wear, noise, and improving the operational reliability of mechanical systems with clearance couplings.