Restriction of Propagation of Nonlinear Spatio-Temporal Vibration in Magnetically Levitated Elastic Body by Power Electronics Technology

1. 磁弹性体的模型磁悬浮弹性体不受任何机械接触，因而各种振动模式都不受阻尼的影响。特别是分布结构中空间驻波节点的存在，使得磁场对体的支撑变得困难。本课题主要研究磁弹性梁耦合结构和带弹性轴的旋转系统。得到如下结果：(a)数学模型：根据磁弹性梁耦合结构和带弹性轴的旋转系统的实验结果，推导出表征系统动力学行为的数学模型。对于耦合结构，根据磁分布周期对传统偏微分方程进行空间离散。采用多体表示方法对具有弹性轴的旋转系统在旋转运动下进行建模。(b)数值模拟：对数学模型进行数值研究。稳定波和不稳定波的多样性共存于磁弹性梁系统的行为中。给出了带节点的不稳定波解与钟摆局部振动的关系。明确了弹性轴旋转系统旋转运动中跳跃现象的动力学机理。基于电力电子技术的波传播稳定实验研究在磁悬浮弹性结构中配置了一套阻尼弹性波传播的实验系统。电力电子电源电流中的高次谐波使系统产生悬浮不稳定性。电磁铁的位置对稳定波的传播非常重要。实验结果为弹性结构磁悬浮系统的设计提供了依据。

1. Model of Magneto-Elastic BodyA magnetically levitated elastic body is free from any mechanical contact such that the variety of vibration modes appears without damped. Especially, the nodes of spatial standing waves in the distributed structure make it difficult to support the body by magnetic force. In this project, the coupled magneto-elastic beam structure and the rotating system with elasitc shaft are mainly studied. The following results are obtained.(a) Mathematical Model : Based on the experimental results which obtained in the coupled magneto-elastic beam structure and the rotating system with an elastic shaft, mathematical model which can represent the dynamics of the system behavior was deduced. As for the coupled structure, the conventional partial differential equation was spatially discretized according to the period of the magnetic distribution. The rotating system with an elastic shaft was model by using multi body representation under the whirling motion.(b) Numerical Simulation : The mathematical models were numerically studied. The variety of stable and unstable waves coexists in the behavior of magneto-elastic beam system. The relation between the unstable wave solution with a node and the local vibration of the pendulum was clearly shown. The dynamical mechanism of the jump phenomenon in the whirling motion of the rotating system with an elastic shaft is clearly explained.2. Experimental Study based on Power Electronics for Stabilization of Wave PropagationAn experimental system was configured for damping the elastic wave propagation in the magnetically levitated elastic structure. The higher harmonics in the current of power electronics power source gives the system the instability of levitation. The location of electric magnet is important to stabilize the wave propagation. The experimental results are clues to design the magnetic levitation system of elastic structure.