透過您的圖書館登入
IP:44.213.80.203
  • 學位論文

雙擺長調諧質量阻尼器之減振效益與人行橋振動分析之研究

Effect of Vibration Reduction of Suspension Typed Tuned Mass Damper with Double Pendulum Lengths and Analysis of Footbridges on Pedestrian Induced Vibration

指導教授 : 鍾立來

摘要


懸吊式調諧質量阻尼器(Tuned mass damper ,TMD)一般實務上,都視為小角度擺動、線性回復力,但實際上擺動角度太大,回復力進入非線性,TMD的頻率會下降,會影響其調諧減振的能力,本文第二章即推導單擺長TMD的非線性運動方程式,並運用狀態空間法,轉入離散時間的狀態差分方程式,以求解非線性單擺在每一個瞬間的歷時反應,探討其線性與非線性的回復力、頻率的相對誤差,並以線性與非線性的運動方程式計算結果,觀察進入非線性後,對外力敏感度和設計參數敏感度的影響。綜合分析的結果,TMD擺角過大,確實會令減振效果下降,但需要在非常強的外力激振下才會有如此劇烈的擺動,所以說在一般的工程案例下,將TMD視為線性作設計是合理的。 一般懸吊式TMD機構只有單一個擺長,所以進行最佳化設計時,僅以在外力激振下,結構反應較大的方向去進行最佳化設計,若結構雙向頻率差異較大,且受外力激振下,雙向的反應也相當時,單一擺長並不足以滿足要求,所以,本文中提出單一個TMD具雙擺長的機構,一個TMD就可以同時調諧到結構兩個方向的頻率。分析方法,從雙擺長TMD的運動曲面方程式建立開始,曲面梯度最陡的方向即為回復力的方向,回復力的大小便為曲面梯度的函數,也經由運動曲面,可推得裝設在TMD上的阻尼器兩端的相對速度,即可求得阻尼力,回復力與阻尼力均為非線性,再把此回復力與阻尼力投影到運動方程式建立的兩個水平方向上,就可以建立完整的雙擺長TMD運動方程式,也藉由狀態空間求解此運動方程式,模擬其動力反應。第四章的案例分析,是高樓加裝TMD的設計案例,因為結構頻率差異不太且反應全由單一方向主控,所以原案由單一擺長設計,完全能達到減振要求。本文主要為了彰顯雙擺長設計的優異性,所以會以人為的方式將結構變異,讓結構雙向在不同的頻率比下作設計,並調整風力,比較單擺長與雙擺長設計的差異,結果顯示,以雙擺長調諧確實有比較好的減振效果。 本文的最後一部分,第五章,會以人行橋人行載重引致的振動進行研究,是因為近來結構材質講求輕質材料,且人行橋講求美觀與新穎的設計風格,所以人行走所造成的振動問題也越來越重要。國內對人行橋的振動案例分析沒有一套較清楚完整的參考範本,所以本文參考國外相關研究與規範之人行載重的模擬、作用於橋上的群體載重的特性等,將整理出來的分析程序應用於一個實際案例,整理一套程序,以供相關設計參考。

並列摘要


A simple pendulum consists of a mass which hangs from a string and fixes at a pivot point. By applying Newton's secont law, the equation of motion for the pendulum could be obtained. In this study, the nonlinear and linear equation of motion of a pendulum and pendulum-structure system subjected to external forces is derived. The time history analysis is simulated using state-space method. The amplitude of angular displacement is small so that the equation of motion could be reduced as a simple harmonic equation of motion. This assumption is confirmed by comparing the time history analysis, frequency sensitivity analysis, and design parameter sensitivity analysis results. Passive tuned-mass dampers (TMDs) are a very efficient solution for the control of structural vibrations subjected to long-duration, narrowband excitations. In this study, a suspension typed tuned mass damper with double pendulum lengths is proposed. The pendular mass is suspensed by cables and linked with viscous dampers. The main advantage of the proposed double pendulum lengths TMD is that, it allows control of structural vibrations in both principal directions with different natural frequencies. Numerical results show that, under various wind force excitations, the level of response reduction achieved by the proposed double pendulum lengths TMD is much better than a single pendulum lengths TMD in both directions. Vibration behavior of the footbridge due to pedestrian loading has arised the attraction in these years. The cases of London Millennium bridge, Toda Park bridge in Japan, etc… show that the dynamic action of pedestrian loading should be taken into consideration in design procedures. According to those European footbridge design codes and some relative researches, the method of modeling pedestrian loadings acting on the footbridge is accomplished. Analysis and design procedures of a practical footbridge vibration reduction by TMD is performed in this study. These evaluation methods of footbridge vibration reduction are proposed for engineering applications.

參考文獻


[13]、連冠華、鍾立來、吳賴雲 “可變擺長單擺式調諧質塊阻尼器之半主動控制”
[14]、鍾立來、吳賴雲、賴勇安. “應用相位控制原理於調諧質塊阻尼器最佳化結構控制設計”
[15]、鍾立來、吳賴雲、林美君. “結構具單一非線性調諧質塊阻尼器最佳化設計於將低風力反應之研究”
[12]、吳軒宇、陳永祥 ”應用調諧質量阻尼器及調諧液柱阻尼器於台北101大樓
[10]、鍾立來、吳賴雲、林廷翰. “雙擺長摩擦單擺型調諧質量阻尼器減振效益之

延伸閱讀