鍾立來Chung, Lap-Loi臺灣大學:土木工程學研究所林廷翰Lin, Ting-HanTing-HanLin2010-06-302018-07-092010-06-302018-07-092009U0001-2007200903295600http://ntur.lib.ntu.edu.tw//handle/246246/187724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。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.口試委員審定書 i 要 iibstract iii 錄 1 片 目 錄 3 目 錄 3 目 錄 4一章 緒論 14.1 研究動機及目的 14.2 文獻回顧 16.3 本文內容 20二章 雙向摩擦鐘擺型TMD之動力行為 21.1 曲面之斜率 21.2 雙向FPS型TMD之回復力與最大摩擦力 22.3 雙向FPS型TMD之動力方程式 26.4 雙向FPS型TMD摩擦力之計算 29三章 雙向摩擦鐘擺型TMD之案例分析 35.1 雙向FPS型TMD於自由振動下之動力行為 35.2 雙向FPS型TMD於外擾動下之動力行為 37.2.1 雙向FPS型TMD於週期波擾動 37.2.2 雙向FPS型TMD於地表加速度擾動下之動力行為 39四章 結構加裝雙向摩擦鐘擺型TMD之動力行為 41.1 雙向結構系統之動力方程式 41.2 雙向結構系統加裝雙向FPS型TMD之動力方程式 42.3 摩擦力之計算 46.4 最佳設計參數分析 51.4.1 僅X方向單獨分析 54.4.2 僅Y方向單獨分析 55.4.3 雙向FPS型TMD之最佳設計參數與歷時分析 56五章 實例分析 59.1 臺北101大樓結構系統簡介 59.2 雙向結構系統加裝雙向FPS型TMD之案例分析 60.2.1 等曲率雙向FPS型TMD對於雙向同頻率結構之減振 60.2.2 變曲率雙向FPS型TMD對於雙向同頻率結構之減振 62.2.3 等曲率雙向FPS型TMD對於雙向不同頻率結構之減振 65.2.4 變曲率雙向FPS型TMD對於雙向不同頻率結構之減振 69.3 減振效益比較 74六章 結論與展望 77.1 結論 77.2 展望 79考文獻 805068611 bytesapplication/pdfen-US調諧質塊阻尼器雙向摩擦鐘擺系統非線性tuned mass damper (TMD)bidirectionalFPSnonlinearthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/187724/1/ntu-98-R96521230-1.pdf