带有双侧刚性约束的两自由度振动系统的动力学分析

Dynamics of a two-degree-of-freedom vibration system with bilateral rigid stops

研究了带有双侧刚性约束的两自由度受迫振动系统的动力学特性,推导了对称刚性约束振动系统对称型n-1-1振动的解析式及其Poincaré截面不动点的扰动映射,确定了不动点扰动映射的Jacobi矩阵,讨论了对称型n-1-1振动的不稳定性与局部分岔。基于多参数、多目标协同仿真分析揭示了振动系统低频域内基本周期冲击振动群、非完整颤振冲击振动、完整颤振冲击振动的特征及形成过程,探讨了相邻基本周期冲击振动相互转迁的不可逆性及其伴随的系列奇异点、迟滞转迁域和舌形转迁域的发生机理,发现了舌形转迁域内亚谐冲击振动的模式类型及特征规律。分析了带有非对称刚性约束的受迫振动系统在不同间隙阈值条件下周期、亚谐冲击振动的模式类型及发生区域,对比分析了带有对称和非对称刚性约束振动系统低频域内周期、亚谐冲击振动的模式类型、分布规律和分岔特征的异同性。

The dynamics of a two-degree-of-freedom vibration system with bilateral rigid stops was studied.The analytic experssion of the symmetrical n -1-1 motion and disturbed map of the Poincaré section at the fixed point of the periodically-forced system with symmetric rigid stops were derived.The Jacobi matrix of the disturbed map at the fixed point was determined.The instability and local bifurcation of the period n single-impact symmetrical motion were discussed.The distribution and formation of the fundamental period group of impact motions,the incomplete and complete chattering-impact motions of the vibration system in low frequency region were revealed by the multi-target and multi-parameter co-simulation analysis.The irreversible transition process between adjacent impact motions with fundamental period and the mechanism of hysteresis and tongue-shaped regions,as well as a series of singularities were discussed.Pattern types and characteristic laws of sub-harmonic impact motions were found in the tongue-shaped regions.Pattern types and existence regions of different periodic-impact motions of the vibration system with asymmetric bilateral stops under different clearance thresholds were analyzed.Pattern types,distribution and bifurcation characteristics of sub-harmonic impact motions in the tongue-shaped regions of the two kinds of periodically-forced vibration systems with symmetric and asymmetric stops were compared analytically.