Nonlinear dynamics and chaotic control of a flexible multibody system with uncertain joint clearance

The nonlinear dynamics of a flexible multibody system with interval clearance size in a revolute joint is investigated in this work. The system is modeled by using a unified mesh of absolute nodal coordinate formulation (ANCF), that is, the flexible parts are meshed via the finite elements of the ANCF and the rigid parts are described via the ANCF reference nodes (ANCF-RNs). The kinetic models of all revolute joints are formulated by using ANCF reference node (ANCF-RN) coordinates. The influence of the Lund-Grenoble and the modified Coulomb’s friction models on the system dynamics is comparatively studied. The Chebyshev tensor product sampling method is used to generate the samples of the interval clearance size. With the purpose to maintain the continuous contact of the clearance joint, a modified extended delayed feedback control (EDFC) is used to stabilize the chaotic motion of the flexible multibody system. Finally, the dynamics of a planar slider–crank mechanism with interval clearance size in a revolute joint is studied, as a benchmark example, to check the effectiveness of the presented computation method and the modified EDFC.