雙向摩擦鐘擺型調諧質塊阻尼器減振效益之研究

The Effect of Vibration Reduction of Bidirectional Friction Pendulum System Typed Tuned Mass Damper

林廷翰(Ting-Han Lin)

指導教授 ： 鍾立來

共同指導教授 ： 吳賴雲(Lai-Yun Wu)

國立臺灣大學/工學院/土木工程學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.02142

摘要

本文旨在探討雙向結構系統加裝雙向FPS型TMD之動力行為及其減振效益，以雙向結構系統加裝單一雙向FPS型TMD為分析對象。當結構物雙向振動頻率不同時，雙向FPS型TMD可依結構雙向不同之振頻分別設計不同之曲率半徑，分別進行調頻，使FPS型TMD雙向之振動頻率與結構雙向振動頻率相調諧，以達到減振效果。首先，建立雙向FPS型TMD之滑動曲面方程式，詳述雙向FPS型TMD之力學行為及動力推導過程，其回復力與摩擦力皆為非線性，隨著質量塊移動位置不同而改變。將二階動力平衡方程式轉換成一階狀態方程式，再求得離散時間系統之一階差分狀態方程式進行動力分析。至於摩擦力之計算，以一個方程式囊括兩種滑動行為 (滑動狀態與非滑動狀態) 而求出摩擦力。先模擬雙向FPS型TMD於自由振動、強迫振動及地表加速度擾動下之動力行為，先瞭解雙向FPS型TMD之特性，再模擬一雙向結構系統加裝雙向FPS型TMD，以結構歷時平方和之最小化作為訴求，透過MATLAB現有之最佳化工具：直接搜索法 (Direct Search Method)，搜尋雙向FPS型TMD之最佳設計參數；最後，以臺北101大樓作為實例分析對象，將其雙方向各自單自由度化後作為雙向結構系統，模擬臺北101加裝雙向FPS型TMD之動力行為，驗證雙向FPS型TMD之可行性，並探討當結構雙向振動頻率不同時，等曲率雙向FPS型TMD與變曲率雙向FPS型TMD對於結構減振效果之差異；由臺北101大樓之案例分析可知，當結構雙向之振動頻率相差越大時，越能彰顯出變曲率雙向FPS型TMD減振效果之顯著處。

關鍵字

調諧質塊阻尼器 ； 雙向 ； 摩擦鐘擺系統 ； 非線性

並列摘要

In this study, a bidirectional friction pendulum system (FPS) typed tuned mass damper (TMD) is proposed. If the structural bidirectional natural frequencies are different, by designing bidirectional different the radius of curvature of the bidirectional FPS typed TMD to tuning the TMD frequencies with the structural bidirectional natural frequencies, respectively. At first, conducts the curved surface equation of bidirectional FPS typed TMD, and describes its mechanical behaviors and dynamic equations in detail. The restoring force and friction force both are nonlinear, and varies with the position of the mass. By employing the first order state-space equation transferred from the motion equation of a structure implemented with a bidirectional FPS typed TMD, the discrete-time state-space equation by which the time history analysis can be conducted is derived. In computing friction force, an equation which includes two kinds of motion behaviors (stick and slip states) is proposed. The behaviors of bidirectional FPS typed TMD under free-vibration, forced-vibration and ground motion is simulated, and then implements it on the bidirectional structural system. The design parameters of bidirectional FPS typed TMD are optimized such that the sum of squares of structural response is minimized by direct search method in MATLAB. Finally, the bidirectional FPS typed TMD is implemented on the structure of Taipei 101 such that bi-direction are simplified to single DOF system, respectively. The analytic result shows that when structural bidirectional natural frequencies are different, the vibration reduction of the variable curvature system is better than the fixed curvature system.

並列關鍵字

tuned mass damper (TMD) ； bidirectional ； FPS ； nonlinear

參考文獻

[26] 吳賴雲，鍾立來，張忠信，黃旭輝，陳家乾，“非線性調諧質塊阻尼器設計參數最佳化之研究”，中華民國結構工程學會，結構工程期刊，第23卷，第2期，第107-136頁 (2008)。

[38] 鍾立來，吳賴雲，陳宣宏，黃旭輝，張忠信，林廷翰，“摩擦鐘擺型調諧質塊阻尼器之最佳化設計研究”，國家地震工程研究中心，NCREE 08-018 (2008)。

[4] Den Hartog JP. Mechanical Vibrations. 4th edn, McGraw-Hill, New York (1956).

[5] Warburton GB., and Ayorinde EO. “Optimum absorber parameters for simple systems.” Earthquake Engineering and Structural Dynamics, Vol. 8, pp. 197-217 (1980).

[6] Ayorinde EO., and Warburton GB. “Minimizing structural vibrations with absorbers.” Earthquake Engineering and Structural Dynamics, Vol. 8, pp. 219-236 (1980).