自参数动力系统临界状态减振的非光滑方法

Non-smooth Method for Reducing Vibration of Autoparametric Dynamical System under Critical Condition

系统在达到稳态运动前通常要经历瞬态振动过程。瞬态振动对系统的影响是不可忽略的。在这个过程中作用于系统的激振力频率实际上是由零开始增加到某一工作频率。当激振力频率接近或超过系统的临界频率,系统发生共振,同时振幅达到峰值,并且此共振振幅通常要比系统的稳态振幅大的多。考虑到上述问题,文中分析了两种通过调制激振频率来实现降低临界振幅的方法,即让激振频率按单调线性增加或者分段线性增加到系统工作频率,通过系统相位的调制来实现减振。数值仿真结果表明上述方法能有效地降低临界振幅。同时上述方法工程实际应用中易于实现。

The system usually has transient vibration before it reaches the stable motion. The influence of the transient vibration on the system is not obviously neglectable. During this course, the frequency of the excitation is increased from zero (starting up) to the operation one. When the frequency of the excitement approaches or passes through the critical frequency of the system, the resonance will happen and the vibration amplitude will reach its maximum. In considering of these problems, two methods for modulating the excitation frequency were investigated to reduce the critical amplitude. The strategy was based on the idea that the excitation frequency can be increased by the linear scheme or the stepwise scheme. In this way, the critical amplitude can be reduced by modulating system phase, consequently. It is proved by numerical simulation that these approaches are effective and can be easily implemented in engineering practice.