Discontinuous Dynamics of a 2-DOF Friction Oscillator with Rigid and Elastic Composite Constraints.

Purpose: The switching of motion states and grazing/sliding motion for an oscillator are typical dynamic phenomena in some discontinuous/non-smooth dynamical systems such as friction/vibro-impact systems with clearance. This work describes the behavior of discontinuous dynamics for a two-degree-of-freedom (2-DOF) frictional collision system with intermediate rigid constraint and unilateral elastic collision under periodic excitation by flow switching theory, where this kind of system considered in this paper can better reflect the actual working conditions of a class of mechanical vibration systems and is few researched at present. Methods: First, the physical model studied in this paper is introduced and analyzed in depth (such as motion state, motion equation, etc.). Second, based on the discontinuity/nonsmoothness of oscillator's movement, the absolute and relative phase planes of oscillator's movement are divided into multiple dynamic domains and dynamic boundaries such that the vector field in each dynamic domain is continuous. Third, according to the difference between the static friction coefficient and the dynamic friction coefficient of the system, the flow barrier which is generated on the velocity boundary and prevents the boundary flow from flowing to the domain is studied. Results: By means of the vector field and G-function, the criteria for the switching of each state of motion on the separation boundaries are obtained. And then, the conversions of some typical movements are more intuitively demonstrated through numerical simulation based on MATLAB software. A multi-body dynamics model of this 2-DOF system is developed in MSC Adams to help us visualize the actual dynamics behavior under real dimensional system parameters and compare it with the foregoing numerical simulation for a group of periodic motion data, and the results are nearly consistent. Conclusion: This work further improves the flow switching theory and brings a theoretical reference for multi-constrained mechanical systems. [ABSTRACT FROM AUTHOR]