一类摩擦振子的纯滑动运动分析

Analysis of pure slip motions of a class of friction oscillator

简单的摩擦振子蕴藏着复杂的粘滑运动。纯滑动运动分析是摩擦振子粘滑运动分析的基础。当摩擦振子中存在粘性阻尼时,其运动复杂程度大大增加。首先给出了其纯滑动运动的精确解,得到了振动幅值的解析表达式。研究发现,对于不同的粘性阻尼比,纯滑动运动的精确解具有相似的结构,可以给出一个统一的解析表达式。并分析了粘滑运动与纯滑动运动的边界,即所谓的ssb(stick-slip boundary)曲线。得到了ssb曲线的曲线方程,为进一步分析粘滑运动打下了基础。最后对解的稳定性进行了分析。

A simple friction oscillator implies a complicated stick-slip motion.The premise or basis of stick-slip motion is pure slip motion.For the pure slip motion of a friction oscillator with two phases and no viscous damping,it has been discussed by many scholars.For a friction oscillator with viscous damping,its complexity increases greatly.An analytic solution of pure slip motion of this system was presented.The amplitude of the pure slip motion could be expressed implicitly.Similar solution structures for different viscous damping ratios could be found.Then,an united form of solutions was obtained for different viscous damping ratios.The bounders of pure slip motions were the borders of stick-slip motions too,which were so called stick-slip boundary(SSB) curves.The analytic expressions of SSB curves were also obtained and discussed,which were important to stick-slip motions.At the end,the stability analysis was presented with the method of Poincare map.