一类多刚性限幅振动系统的动态稳定性分析

doi:10.13229/j.cnki.jdxbgxb20220644

摘要/Abstract

摘要：

建立了一类含有多刚性限幅约束的两自由度受迫振动系统的力学模型。结合系统周期和冲击Poincaré映射，在双参数系内识别出周期冲击运动的模式多样性及其发生域。伴随不连续的擦切分岔，在相邻单周期冲击运动分布域的临界线上存在一系列奇异点、迟滞和舌形转迁域。根据动力学参数的采样范围，分析了极端质量分布工况下振动系统的动态响应。仿真结果表明：在低频区域的单周期冲击运动序列随频率递减，经连续的擦切分岔、滑移分岔等非光滑分岔行为，存在向非完全颤振冲击、完全颤振冲击转迁的形成规律。冲击瞬时的能量损失过大会导致粘滞现象，从而改变振动系统的原结构，降低系统自由度。由于多处刚性约束完全颤振冲击的同时作用，系统在极端参数控制域内会呈现短暂的停滞状态。

关键词: 机械设计, 限幅振动, 分岔, 转迁域, 颤振冲击

Abstract:

The mechanical model of a two-degree-of-freedom amplitude-limited vibration system with multiple rigid constraints is established. Combined with the periodic and impact Poincaré mapping， the pattern types of periodic impact motions and their occurrence domains are identified in a two-parameter system. With the irreversible mutual transition of adjacent one-periodic impact motions， there are a series of singularities， hysteresis and tongue-shaped transition domains on the critical line of the distribution domains. Based on the sampling range of dynamic parameter， the dynamic response of the vibration system under extreme mass distribution conditions is analyzed. The simulation results show that the non-smooth bifurcation behaviors such as Grazing bifurcation and Sliding bifurcation leads to the one-periodic impact motion sequence transits to incomplete and complete chattering-impact motions. Excessive energy loss in instantaneous impact leads to sticking phenomenon， which changes the original structure of the vibration system and reduces the degree of freedom of the system. Due to the simultaneous action of complete chattering-impact at multiple rigid constraints， the transient static state appears in extreme control parameter domain.

Key words: mechanical design, amplitude-limited vibration, bifurcation, transition domain, chattering-impact

中图分类号:

TH113.1

杨艳,侍玉青,张晓蓉,罗冠炜. 一类多刚性限幅振动系统的动态稳定性分析[J]. 吉林大学学报(工学版), 2023, 53(2): 364-375.

Yan YANG,Yu-qing SHI,Xiao-rong ZHANG,Guan-wei LUO. Dynamic stability analysis of a amplitude⁃limited vibration system with multiple rigid constraints[J]. Journal of Jilin University(Engineering and Technology Edition), 2023, 53(2): 364-375.

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