多约束碰撞振动系统的粘滞运动分析

建立了一类多约束两自由度碰撞振动系统力学模型,根据同一时刻粘滞振子的个数,将所研究的模型划分为四种运动系统,并分析了各个系统的运动。在一定的参数下,由于粘滞振子的个数及其进出粘滞状态的先后顺序不同,系统会出现不同类型的周期粘滞运动,对各个运动系统之间的切换及切换条件进行了分析。当系统中所有的振子同时处于粘滞状态,系统会出现暂时的"静止"。通过对碰撞面上振子的受力分析,我们发现当约束分别布置在振子的两侧时,两振子同时粘滞的受力条件不满足,因此不会出现同时粘滞,并给出了证明;当约束位于振子的同一侧时,通过对系统参数的调节,系统会出现暂时"静止"。最后给出了所研究模型的算例验证,并对数值模拟结果进行了分析。

Analysis of sticking motion in a vibro-impact system with multiple constraints

A two DOF vibro-impact system with multi-constraint is established. According to the number of sticking oscillators, the model researched in this paper can be divided into four moving systems, whose motions are analyzed simultaneously. Under certain parameters, different kinds of periodic sticking motions will appear, because of the different number of sticking oscillators and the different start and end time of sticking motion. In this paper, the switchover and transition conditions among the four moving systems are studied. The temporary “stillness” will appear when all the oscillators of the system are in sticking state at the same time. In the impacting surfaces, by analyzing the force applied on the oscillators, we discover that when the constraints are arranged on different sides of the two oscillators, the forces of the two oscillators can’t satisfy the sticking conditions simultaneously, so the simultaneous stick won’t happen and the provability is given. By altering the parameters, temporary “stillness” will appear when constraints are placed on the same sides of the two oscillators. Finally, numerical simulation is given, and the results are also analyzed.