两自由度碰撞振动系统的粘滞运动和隆起现象

STICKING MOTIONS AND RISING PHENOMENA IN THE TWO-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM

考虑了一类两自由度多运动约束的碰撞振动系统力学模型,根据质块碰撞时可能出现的粘滞运动情况,分别求出了各种可能粘滞运动情况时的解析解.通过对粘滞运动判定的必要条件,证明了当约束分别位于质块的异侧时,两质块不会出现同时粘滞的运动,即所谓的暂时"静止"状态.当约束分别位于质块的同侧时,通过对参数的调整,可能出现同时粘滞的暂时"静止"状态.最后通过数值计算,分别在考虑的两种情况中,对于外激励频率较小时,验证了周期粘滞运动.并且在约束位于质块的同侧时,模拟出了两质块同时粘滞的暂时"静止"状态,对于约束分别位于两质块的异侧时,模拟出了周期粘滞运动和所谓的隆起现象.由数值计算可以看到,暂时的"静止"状态一般是由两个质块分别先后进入和离开粘滞运动而发生和结束的,而不是两个质块同时粘滞和同时结束.

A class of two-degree-of-freedom multiple constraint mechanics model of the vibro-impact system was considered. According to the oscillator possible sticking situation, the explicit solution of every possible situation was worked out. Through the sticking motion＇ s necessary condition, we prove that the two oscillators wont appear sticking at the same time when the constraints are in different side. When constraints are located in the same side, by adjusting the parameters, the sticking may occur at the same time. That was called temporarily ＂motion- less＂ situation. Finally, numerical calculation verified the cycle sticking motion and rising phenomena when the constraints are in different side and temporarily ＂motionless＂ situation when constraints are located in the same side. By numerical calculation, one can see that temporary ＂motionless＂ situation generally happens or ends by two vibrators successively entering or leaving sticking motion. It is not that the two oscillators are sticking or end at the same time.