机械系统的碰撞振动与控制

机械系统内部或边界间隙引起的碰撞振动是机械动力学的研究热点之一。该领域的近期研究成果有:(1)碰撞振动的间断和连续分析,包括稳定性分析、奇异性问题、擦边诱发分叉、非线性模态等研究;(2)碰撞振动控制,特别是不连续系统的控制方法和控制混沌碰撞振动;(3)碰撞振动分析的数值方法;(4)碰撞振动实验研究。

A Prelude Staircase to a Type V Intermittency in Two—Dimensional Discontinuous Maps

A sequence of periodic attractors has been observed in a two-dimensional discontinuous map, which canbe considered as a model of impact oscillator. The so-called 'transfer number', which is defined as the mean numberof transfer from non-impact state to impact state per iteration, is locked onto a lot of rational values to form a curveconsisting of many steps. Our numerical investigation confirms that every step is confined by conditions created by thecollision between the periodic orbit and the discontinuous boundary of the system. After the last collision the systemshows a chaotic motion with intermittent characteristics. Therefore the staircase can be addressed as a 'prelude staircaseto type V intermittency'. The similar phenomenon has also been observed in a model of electric circuit. These resultsof our study suggest that this kind of staircases is common in two (or even higher) dimensional discontinuous maps.

高功率超声脉冲激励下金属板的非线性振动现象研究

对高功率超声脉冲作用下金属板中的超谐波、次谐波、准次谐波以及混沌等非线性振动现象进行了实验和理论研究.在实验中,高功率超声换能器产生脉冲调制的高频振动激励金属板产生非线性振动,利用激光测振技术测量不同尺寸和不同固定方式下金属板复杂的非线性振动情况,并对其进行了时序分析、频谱分析以及相空间分析.根据实验条件,提出包含非线性接触阻尼的振动-碰撞动力学模型,用以研究强超声振动-碰撞作用下的板非线性振动机制,并进行了相应的理论计算.计算结果表明,超声换能器的变幅杆与金属板之间的间歇性高频碰撞作用是金属板强非线性振动的主要原因.数值计算结果与实验测量结果符合很好.