一类单自由度双侧含约束的碰撞振动系统动力学研究
Dynamics Study of a Class of Single Degree of Freedom Double-Sided Constrained Collision Vibration Systems
DOI: 10.12677/dsc.2025.141001, PDF,   
作者: 李沛民, 李道权, 张 惠：兰州交通大学机电工程学院，甘肃 兰州
关键词: 非对称；吸引域；胞映射；Non-Symmertric； Attraction Domain； Cell-to-Cell Mapping
摘要: 本文研究对一种具有双侧非对称约束的单自由度非对称碰撞振动系统进行了深入探讨。首先，对系统进行了无量纲化处理，并详细分析了其周期运动的分岔类型。接着，本研究推导了系统在周期运动条件下的Jacobi矩阵，并运用参数状态空间联合仿真的方法，系统地探究了系统在参数平面 ( ω ),( ω,δ ) 下的转迁规律及变化参数 ω 时的动力学行为。此外，本文还研究还关注了系统在状态空间中吸引域的存在现象。
Abstract: This study delves into a single-degree-of-freedom asymmetric impact vibration system with bilateral asymmetric constraints. Initially, the system was subjected to a dimensionless transformation, and a detailed analysis was conducted on its bifurcation types of periodic motions. Subsequently, the Jacobi matrix of the system under periodic motion conditions was derived. Utilizing a combined simulation approach of parameter and state space, a systematic exploration was performed on the transition laws of the system in the parameter plane ( ω ),( ω,δ ) and its dynamic behaviors when varying the parameters ω . Additionally, the study also focused on the existence phenomenon of the attraction basins in the state space of the system.
文章引用：李沛民, 李道权, 张惠. 一类单自由度双侧含约束的碰撞振动系统动力学研究[J]. 动力系统与控制, 2025, 14(1): 1-10. https://doi.org/10.12677/dsc.2025.141001

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