Nonsmooth dynamics of a 3D rigid body on a vibrating plate

摘要: In this work, we study a 3D rigid body, which is in shape similar to dumbbell, bouncing on harmonically vibrating plate. The system involves two contact sets whose states vary with the relative motion between plate and dumbbell. These are closely related physical properties of surfaces, can be identified using relationships kinematics. Under certain states, system-singular modes will likely occur due absence tangential compliance Coulomb’s friction. Resolutions for these singularities given, an integrated model, taking hierarchical structure adaptable state variations, has been developed. Within impact-free state, forces drive dumbbell obtained LCP (linear complementary problem) formulation. For impact post-impact outputs serve as initial conditions subsequent calculated based new theory developed dynamics. Specifying bounce vertical plane, model was justified by comparison our results experimental findings other work. As periodic behaviors appear planar dynamics, scenario also reveals intriguing patterns trajectories dumbbell’s mass center projected onto horizontal plane. They include closed circular orbit, dog-legged path, straight line.