Tuned mass dampers for structures with closely spaced natural frequencies
Tuned mass dampers for structures with closely spaced natural frequencies
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DOI：
10.1002/eqe.4290240209
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发表时间：
1995-02
影响因子：
4.5
通讯作者：
M. Abé;T. Igusa
中科院分区：
文献类型：
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作者：
M. Abé;T. Igusa
分析结果可用于具有一个或多个调谐质量阻尼器(TMD)的结构的振动控制。输入是一个具有可能频率范围的谐波负载。控制目标是减小结构响应的最大幅值。摄动理论采用三组小参数：TMD与结构模态质量之比、系统的阻尼值、结构频率与加载频率之差。分析表明，对于固有频率分布较大的结构，其响应可以用著名的单振型结构/TMD系统的响应来精确地逼近。对于具有p个密集固有频率的结构，发展了更一般的解析结果来描述结构的p个振型的运动与多个TMD之间的耦合。结果表明，为了控制结构的响应，至少需要设置p个TMD，并在结构上放置适当的附件。如果使用较少的TMD，则最大频率响应具有与TMD的属性无关的下限。无论结构的固有频率有多大，TMD的位置总是很重要的。给出了集中质量结构和连续结构的计算结果。
Analytical results are developed for vibration control of structures with one or more Tuned Mass Dampers (TMDs). The input is a harmonic load with a range of possible frequencies. The control objective is to reduce the maximum amplitude of the structural response. Perturbation theory is used with three sets of small parameters: the ratio of TMD and structural modal masses, the damping of the system, and the differences between the structural and loading frequencies. It is shown analytically that for structures with widely spaced natural frequencies, the response can be approximated accurately by the response of the well-known single-mode structure/TMD system. For structures with p closely spaced natural frequencies, more general analytical results are developed to describe the coupling between the motions of the p modes of the structure and the multiple TMDs. The results show that at least p TMDs with properly placed attachments to the structure are necessary to control the response. If fewer TMDs are used, the maximum frequency response has a lower bound which is independent of the properties of the TMDs. The TMD placement is shown to be always important, regardless of the spacing of the structure's natural frequencies. The results are illustrated for both lumped-mass and continuous structures.