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標題: 被動調諧質量阻尼器對懸臂樑自由振動減震之最佳化分析
Optimum Passive Tuned Mass Damper Parameters for Free Vibration of A Cantilever Beam
作者: 楊政道
Yang, Zheng-Dao
關鍵字: 質量阻尼器
出版社: 應用數學系
摘要: 在本篇論文內,主要是分析懸臂樑在自由振動時,加上一個被動調諧質 量阻尼器 ( Passive Tuned Mass Damper)後減震之效果。分析的方 式分為兩種:(1)將懸 臂樑視為單一自由度,(2)將懸臂樑分為數段樑 單元。在分析的過程中,利用模態 分析法(Modal analysis)的原理 定義模態下降指數,並以此判斷 PTMD 的效果。 文中發現PTMD與結構之 質量比固定時,PTMD 與結構之無阻尼自然頻率比在 1.0 附 近且 PTMD 的阻尼比大於結構阻尼比時(但並非愈大愈好)有較佳的效果。對低阻 尼結構而言,在 PTMD 質量比很小時,以單一自由度來分析,將有相當大 的誤差。 最後再舉幾個例子來說明最佳 PTMD 參數的效果。
In this paper, the optimum effectiveness analysis of a passive tunedmass damper (PTMD) in reducing a cantilever beam responses under freevibration is studied by using modal analysis and themodal decay index. The cantilever beam is assumed as (1) a single-degree-of-freedom system ; (2) a system with several finite beam elements.With the coupled damping matrix, the eigen- pairs of the system are solvedin complex form. Several optimum PTMD examples are illustrated that thesystem parameters: mass ratio, frequency ratio of PTMD and structure,and the damping ratio of PTMD, and its location in the structure havemajor effects in the performance of system vibration behavior. Thisstudy also shows that with a small mass ratio, the single- degree-of-freedom model have a great error in a structure with lower damping.
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