内嵌自主移动钢球欧拉梁自适应碰撞减振研究

Vibration Suppression via Adaptive Impacts for Euler Beam with Interior Inlaid Freely Moving Steel Ball

结合内嵌自主移动质量子系统梁/板实验平台的实验结果,对共振激励下的内嵌自主移动钢球欧拉梁自适应碰撞减振系统进行了研究.采用弹簧、阻尼表现碰撞过程中的弹性恢复与能量耗散,将碰撞机制转化为线性弹簧-阻尼模型,并基于赫兹接触理论对相关参数进行了估算.通过分析建立了碰撞的开始与结束条件,以及系统的分段线性动力学控制方程,数值计算结果充分表明了内嵌自主移动钢球自适应碰撞减振的内在机理与有效性.在钢球随机碰撞作用下,梁的振动响应为概周期振动,一阶共振激励下单个钢球的碰撞减振效果为7.5%,二阶共振激励下为6.1%.通过与假定钢球在其他位置实施碰撞减振的效果进行比较,证明了内嵌钢球的自适应碰撞减振特性.

Combining the experiments carried out in the experimental workbench for beam and plate with interior inlaid freely moving mass, a self-adaptive impact vibration suppression system, i.e. a Euler beam with an interior inlaid freely moving steel ball under the principal resonant harmonic excitation, is investigated. In the theoretical analysis, a linear spring-damping model is employed to simulate the impact mechanism between steel ball and beam interior walls, where the elastic recovery and energy dissipation in impacts are respectively characterized by the spring and damping in the model, and relative parameters are also determined according to the Hertz contact theory. Then for the impact system, the linear piecewise dynamic equations and the beginning and ending conditions for impacts are all established. Numerical results demonstrate the inherent mechanism and effectiveness of adaptive impact damping for the steel ball in suppressing the beam vibration, and the vibration is reduced by 7.5 % and 6.1 % respectively under the first and second principal resonant harmonic excitations. Moreover, the beam vibration does not get periodic but quasi-periodic. Assuming that the impacts take place on a virtual location instead of the actual lo- cation observed in experiments, the self-adaptive impact damping characteristic is proved for the steel ball.