具有恒定速度的传送带模型全局动力学
Global Dynamics of a Conveyor Belt Model Moving at Constant Velocity
摘要: 本文基于Filippov非光滑动力系统理论，研究了一类置于恒定速度运动传送带上的干摩擦SD振子的全局动力学行为。深入探讨了子系统平衡点的存在性、类型及稳定性。然后，利用Lyapunov函数方法与Filippov凸组合理论，系统分析了全局吸引子的存在性条件，并给出了擦边周期轨与擦边同宿轨发生分岔的充分条件。进一步揭示了在临界参数下，传送带速度对同宿环存在状态及破裂机制的调控作用。通过数值模拟验证了理论分析的有效性。所得结论为含干摩擦几何非线性振动系统的设计与减振控制提供了理论依据。
Abstract: Based on the Filippov’s theory of non-smooth dynamical systems, this paper studies the global dynamic behavior of a class of dry-friction SD (Smooth and Discontinuous) oscillators placed on a constant speed motion conveyor belt. The existence, type and stability of the balance point of the subsystem are discussed in depth. Subsequently, using the Lyapunov function method and Filippov’s convex combination theory, the system analyzes the existential conditions of the global attractor, and gives the sufficient conditions for the splitting of the edge period track and the edge and the sleep track. It further reveals the regulatory effect of the conveyor belt velocity on the state of existence and the rupture mechanism of the same boarding track under critical parameters. The validity of the theoretical analysis is verified through numerical simulations, and these conclusions obtained provide a theoretical basis for the design and vibration damping control of the geometric split-line vibration system with dry friction.
文章引用：罗勇顺. 具有恒定速度的传送带模型全局动力学[J]. 应用数学进展, 2026, 15(10): 229-246. https://doi.org/10.12677/aam.2026.1510411

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