Periodic orbits and bifurcation of a two-degree-of freedom dry friction coupled vibration system

Abstract This article explores the dynamic behavior of a two-degree-of freedom dry friction coupled vibration system. By constructing a generalized Poincaré map and obtaining the necessary and sufficient conditions for the existence of invariant cone in the system, the linearization principle of Poincaré map is equivalently replaced by the study of a global monodromy matrix. Based on the Floquet theory, the stability of the invariant cone consists of periodic orbits is proved, and the bifurcation phenomenon and persistence of the invariant cone under parameter changes are explored. The distribution configuration of the trajectory is given through numerical simulation, verifying the accuracy of the theory. This provides a theoretical basis for parameter optimization and vibration control of high-dimensional dry friction vibration systems in practical engineering applications.