非線性調諧質量阻尼器於建築結構中之最佳化設計與耐震性能研究

Optimal Design and Performance Evaluation of Nonlinear Energy Sink for Buildings under Seismic Excitation

孫濤(Tao Sun)

指導教授 ： 張家銘

國立臺灣大學/工學院/土木工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202000080

摘要

調諧質量阻尼器(Tuned Mass Damper, TMD)是目前被廣泛接受的被動控制 系統,因多以線性彈簧作為調頻機制,而受限於單一頻率。本研究以非線性調諧質 量阻尼器(Nonlinear Energy Sink, NES)提供幾何非線性回復力作為理論基礎,藉 由質量塊在兩段半徑大小不同之圓規上滑動,實現多頻率調頻機制;另外,在軌道 兩側設置黏彈性材料擋板,以限制 NES 位移。並利用非線性黏彈性碰撞模型,模 擬鋼球與黏彈性材料碰撞產生的力量。本研究將此非線性系統於 Matlab 建立數值 模型,採用四階-五階 Runge-Kutta 法進行運動方程求解,進而得到精確的模擬結 果。
根據 8 個符合反應譜之地震頻率特性與具常態分佈之亂數,合成 10 個人造地 震。考量舒適度、中小地震及超越地震 3 種強度之外力,以分段設計的概念,期待 遭受較小地震時,NES 只在第一段圓軌運動,與線性 TMD 有相似之控制效果;遭 受中小地震時,NES 能運動至第二段圓軌,使 NES 產生類似勁度硬化或軟化效應; 遭受超越地震時,NES 將與黏彈性擋板發生碰撞,利用碰撞力與粘彈性擋板的塑 性形變對結構加以控制與效能。並以 10 個人造地震之結構位移反應平均值,作為 設計指標。探討單自由度剪力構架及美國土木工程學會(American Society of Civil Engineers, ASCE)提供的 20 層 Benchmark Building 加裝 NES 之最佳化參數。以 及對具有最佳參數之 NES,在真實地震力作用下進行耐震性能評估。

關鍵字

被動控制 ； 非線性調諧質量阻尼器 ； 非線性黏彈性碰撞模型 ； 標準建築結構 ； 地震力

並列摘要

In this study, Nonlinear Energy Sink(NES) is used to provide a geometrically non- linear restoring force as a theoretical basis. A multi-frequency tuning mechanism is realized by two circular orbits with different radiuses. In addition, two sides of the orbit applied viscoelastic material baffle to limit NES displacement. The nonlinear viscoelastic collision model is used to simulate the force generated by the collision between steel ball and viscoelastic material.
Based on 8 seismic frequency characteristics that fit the response spectrum, 10 artificial earthquakes were synthesized. Taking into account three levels of external force: the comfort, the small-medium earthquakes, and exceedance earthquakes, with the concept of segment design, it is expected that when a small earthquake is encountered, the NES will move in the first section of the circular track; when it is subjected to a small- medium earthquake, the NES can move to the second section of circular track and make the stiffness of NES stiffen or soften; when it is subjected to an exceedance earthquake, the NES will collide with a viscoelastic baffle. The average displacement response value of 10 man-made earthquakes is taken as the design principle. The optimal parameters of the 20-story Benchmark Building retrofitted with NES provided by the American Society of Civil Engineers (ASCE) and the control effect under real earthquakes were discussed.
The result shows that NES has similar control effects to TMD when subjected to minor earthquakes; NES non-linear mechanism will appear when subjected to small- medium earthquakes; NES will collide when subjected to exceedance earthquakes. In general, compared with the empty structure, it has obvious control effect.

並列關鍵字

Passive control ； NES ； Nonlinear viscoelastic collision model ； Benchmark building ； Earthquakes

參考文獻

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