Dynamic Behaviors of a Two‐Degree‐of‐Freedom Impact Oscillator with Two‐Sided Constraints

Abstract

The dynamic model of a vibroimpact system subjected to harmonic excitation with symmetric elastic constraints is investigated with analytical and numerical methods. The codimension-one bifurcation diagrams with respect to frequency of the excitation are obtained by means of the continuation technique, and the different types of bifurcations are detected, such as grazing bifurcation, saddle-node bifurcation, and period-doubling bifurcation, which predicts the complexity of the system considered. Based on the grazing phenomenon obtained, the zero-time-discontinuity mapping is extended from the single constraint system presented in the literature to the two-sided elastic constraint system discussed in this paper. The Poincare mapping of double grazing periodic motion is derived, and this compound mapping is applied to obtain the existence conditions of codimension-two grazing bifurcation point of the system. According to the deduced theoretical result, the grazing curve and the codimension-two grazing bifurcation points are validated by numerical simulation. Finally, various types of periodic-impact motions near the codimension-two grazing bifurcation point are illustrated through the unfolding diagram and phase diagrams.

Two-parameter cooperative intelligent optimal control of chaotic motion for a vibro-impact system with soft constraint

“…Non-smooth systems with clearance exist widely in mechanical systems, and collisions between components due to the presence of clearance usually lead to nonlinear phenomena such as bifurcation and chaos (Ding et al, 2004; Ma et al, 2012). In order to suppress or reduce the damage of mechanical components caused by chaotic motion and the noise hazards induced, researchers have explored and studied the mechanism of chaotic motion formation and chaotic motion control (Moraes et al, 2013; Du et al, 2018; Zukovic et al, 2021; Souza et al, 2005, 2008; Li et al, 2021; LÜ and Luo, 2020), which has provided certain theoretical and application references for the structural optimization design and chaotic vibration control of mechanical systems with clearance.…”