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In this paper, the discontinuous dynamics in a 2-DOF (two-degree-of-freedom) vibro-impact system with dry friction is investigated by using the flow switchability theory for discontinuous dynamical systems. Multiple domains and discontinuous boundaries are defined according to friction and impact discontinuity. Based on above domains and boundaries, the onset and disappearance conditions of sliding-stick motion are developed and the analytical conditions of side-stick motion and grazing motion are obtained mathematically. The switching sets and mapping structures are adopted to describe the complex motions in such discontinuous system. The numerical simulations are also given to illustrate the analytical results of motion switching on different boundaries. This investigation can help us understand the motion switching mechanism in non-stick, sliding-stick or side-stick motions of the oscillator with friction and impact.

In this paper, complex discontinuous dynamics of a periodically forced double-belt friction oscillator are investigated using the theory of flow switchability for discontinuous dynamical systems. Phase plane of such a system is divided into different domains and boundaries due to the discontinuity caused by the friction and the positions of belts. The analytical conditions of the passable, stick and grazing motions on the corresponding discontinuous boundaries are derived for motion switching complexity in detail. Based on the discontinuous boundaries, switching sets and basic mappings are introduced to describe different periodic motions in such a discontinuous dynamical system. The analytical predictions and corresponding local stability analyses for the periodic motions are developed through mapping structures. Stick and non–stick periodic motions with different mapping structures, stick motions and grazing motions on different discontinuous boundaries are presented numerically for a better understanding of physics of the double–belt friction oscillator.

In this paper, the dynamical behaviors of a friction–induced oscillator with switching control law are studied through the flow switching theory of discontinuous dynamical systems. The physical model consists of a mass on the conveyor belt and a spring-damping system with switching control law. Based on the switching control law and the friction between the oscillator and the conveyor belt, multiple domains and discontinuous boundaries are defined. The G–functions are introduced to illustrate the motion switching mechanism and the analytical conditions of the passable motion, stick motion, sliding motion and grazing motion are presented for motion switchability. The switching sets and mapping structures are adopted to describe the complex motions in this discontinuous system. The numerical simulations are also carried out from the analytical conditions and mapping structures in order to better understand the motion switching complexity of this oscillator.

In this paper, by using flow switching theory of discontinuous dynamical systems, the discontinuous dynamic behavior of a 2-DOF (two-degree-of-freedom) friction oscillator with elastic impact and rigid impact on different sides is investigated. For the 2-DOF friction oscillator, when the direction of object’s velocity changes, the negative feedback works and the inequality of maximum static friction force and kinetic friction force leads to the existence of flow barriers. In addition, the elastic impact and rigid impact can change motion states of object, resulting in the discontinuity of this 2-DOF system. Considering the multiple motion states of object and better analyzing the equation of object’s motion, the phase space of each object is divided into different motion domains and boundaries in relative and absolute coordinates by means of the discontinuities resulted from the friction and impact. Moreover, because the elastic impact exists in a time period, there will be a variety of motion behaviors coexisting, such as elastic and rigid impacts occur simultaneously. With that in mind, in absolute coordinate system, the phase space of the system is divided in six cases according to whether there are stick motion and stuck motion. Based on flow switching theory, the switching conditions at discontinuous boundaries for all possible motions are given by using G-functions, and it should be noted that the vanishing conditions of the sliding motion become more complicated due to the existence of flow barriers at speed boundaries. Through defining the switching sets on separation boundaries, the mapping structures are further introduced to demonstrate the global dynamic behavior and periodic motions. For a better understanding of the object’s motion and the switching criteria at separation boundaries, the numerical simulation method is used to demonstrate several typical motions such as passable motion, sliding motion, grazing motion, stick motion (elastic impact), rigid impact and periodic motions etc. The results obtained have reference value for the optimization design and noise control of mechanical systems with gap couplings and negative feedbacks.

By using the flow switchability theory in discontinuous dynamical systems, this paper deals with the discontinuous dynamical behaviors of a two degrees of freedom system with asymmetric damping, where considering that friction and impact coexist and the static and dynamic friction coefficients are different. Because of the particularity of friction force, the flow barriers on the velocity boundary that affect the leaving flow are considered in this paper. Based on discontinuity that is caused by the sudden change of friction force or the collision between two objects, the phase space of motion for the object is divided into several different domains and boundaries; and with the help of the analysis of vector fields and G-functions on the corresponding discontinuous boundaries or in domains, the analytical conditions for all possible motions are obtained, which is used to determine the switching of motion state in this system. Finally, numerical simulations are presented to better understand the analytical conditions of the stick, grazing, impact, stuck and periodic motions.