Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments
Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments
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DOI：
10.1007/s11071-017-3779-4
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发表时间：
2017-09
影响因子：
5.6
通讯作者：
A. Papangelo;M. Ciavarella;Norbert Hoffmann;Norbert Hoffmann
中科院分区：
文献类型：
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作者：
A. Papangelo;M. Ciavarella;Norbert Hoffmann;Norbert Hoffmann
利用速度弱化-摩擦强化定律研究了单自由度摩擦振动系统的动力学行为，特别关注了亚临界Hopf分叉的所谓硬效应的可能性。以皮带速度为分叉参数，对系统的分叉图进行了数值计算。采用标准线性稳定性分析和大摄动下的非线性稳定性分析，给出了分析结果。前者允许识别完全滑动解稳定的最低皮带速度，后者允许先验地估计存在大幅度粘滑振动的最高皮带速度。这两个边界共同定义了两个平衡解共存的范围，即稳定的完全滑移解和稳定的粘滑极限环。该模型用于与最近的实验观测结果相吻合。
The dynamical behavior of a single-degree-of-freedom system that experiences friction-induced vibrations is studied with particular interest on the possibility of the so-called hard effect of a subcritical Hopf bifurcation, using a velocity weakening–strengthening friction law. The bifurcation diagram of the system is numerically evaluated using as bifurcation parameter the velocity of the belt. Analytical results are provided using standard linear stability analysis and nonlinear stability analysis to large perturbations. The former permits to identify the lowest belt velocityat which the full sliding solution is stable, the latter allows to estimate a priori the highest belt velocity at which large amplitude stick–slip vibrations exist. Together the two boundariesdefine the range where two equilibrium solutions coexist, i.e., a stable full sliding solution and a stable stick–slip limit cycle. The model is used to fit recent experimental observations.