冲击/周期载荷作用下分布式调谐质量阻尼器对响应控制的影响

Influence of Multiple Tuned Mass Damperson Response Control under Impact/Periodic Load

本文研究了采用分布式调谐质量阻尼器(TMD)对悬臂梁进行振动抑制的问题。首先建立了安装N个TMD的悬臂梁的动力学方程;然后通过有限单元法离散偏微分方程,使用Newmark-β法进行含TMD的悬臂梁动响应求解;最后基于数值计算模型,分别研究周期荷载与冲击荷载作用下,梁振动控制的效果。研究表明:TMD可以有效抑制悬臂梁振动,在周期荷载作用下,悬臂端位移降低52%,在冲击荷载作用下,悬臂端最大位移降低12.31%。关于TMD的分布形式:当使用一个TMD抑制振动时,建议TMD的自振频率应与悬臂梁一阶弯曲频率相等,且最好安装在悬臂端部。采用多个TMD可以提高控制效果,但平均单个TMD抑制效果降低。

The vibration control problem of a cantilever beam using multiple tuned mass dampers(TMD) is studied. First,the dynamic partial differential equations of the cantilever beam with N tuned mass dampers are established. Second,the partial differential equations are discretized by using the finite element method,and the Newmark-β method is used to solve the dynamic response of a cantilever with TMD. Finally,the effects of cantilever beam vibration control under periodic load and impact load are explored desparately based on the numerical calculation model. The results show that the proposed TMD approach can effectively suppress the beam vibration. Under the cyclic load,the displacement of the cantilever end can be reduced by 52%,while the maximum displacement of the cantilever end can be reduced by 12.31% under the impact load.Regarding the distribution of TMD:If only one TMD is used,it is recommended that the natural frequency of the TMD should be equal to the first-order bending frequency of the cantilever beam and it should be installed at the cantilever end. Using multiple TMDs can increase the overall control effect,but the suppression effect of average single TMD is reduced.