橋梁動態載重識別之模態函數法

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劉傳騰(Chuan-Teng Liu) 查詢紙本館藏

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土木工程學系

論文名稱

橋梁動態載重識別之模態函數法
(Dynamic Loadings Identification of Bridge by the Modal Function Method)

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摘要(中)

車輛超載容易對公路或橋梁結構等交通設施產生破壞，尤其對於某些交通量大的重要公路或橋梁更顯得重要，基於運輸安全的重要性，因此衍生出許多車輛載重識別(Weigh-In-Motion)的方法，其中一種研究車輛與橋梁之間的力學互制關係，稱之為橋梁動態載重識別方法(Bridge Weigh-In-Motion)，此方法主要利用橋梁的力學反應之應變值來識別出通過之車輛總重及軸重。
本研究主要是利用結構動力方程式做為基礎，並將所分析之橋梁有限元素化，推導出自由度與應變之間的關係，並利用模態的觀念，將自由度展開成模態振形(mode shape)乘上廣義座標，此方法減少反算程式在迭代求解的所耗費的大量計算時間，並可將所量測到的應變值做一個即時(Real-time)分析的應用。藉由引入線性離散時間系統(Linear Discrete-Time System)裡面的狀態空間系統(State-Space System)和在線性代數中求解近似值的一種方法為直接正規化法，如Tikhonov正規化，並利用動態規劃(Dynamic Programming)演算法迭代進行反算求解出橋梁上的移動載重。
橋梁結構數值模擬是利用有限元素法來分析，從二維梁元素模型，到三維梁元素模擬，驗證此動態反算理論利用模態函數法識別載重之準確度，並考量其他因素例如車速，應變計數量等對於載重識別結果之影響探討。

摘要(英)

Overloaded vehicles are prone to produce damage on the road or the bridge structures,especially for the high traffic flow in the important roads or bridges, Based on the importance of transportation safety, many vehicles load identification method (Weigh-In-Motion) are reported recently.One study of the mechanical interaction between the vehicle and the bridge, called the bridge of dynamic load identification methods (Bridge Weigh-In-Motion), the main advantage of this method is using the mechanical strain response of bridges to identify the vehicle′s total weight by and axle load.
This study is based on the equations of dynamic structures and derive the relationship equations between the degree of freedoms and the strains by discretizing the bridge object.and the degree of freedom can be expanded into the modal shape multiplied by the generalized coordinate by using the modal method. This method can reduce a lot of computing time in the inverse program and can make it to be an immediate (Real-time) analysis of the application.
Numerical simulation of the bridge structure is analyzed using the finite element method, from the two-dimensional beam element model to simulate three-dimensional beam elements. To verify the accuracy of the inverse problem by the modal method and to consider influence of the load identification the factors like speed and the number of the strain.

關鍵字(中)

★ 模態法
★ 狀態空間系統
★ Tikhonov正規化
★ 動態規劃

關鍵字(英)

★ modal method
★ state space system
★ Tikhonov regularislation
★ Dynamic programming

論文目次

摘要 I
Dynamic Loadings Identification of Bridge by the Modal Function Method II
誌謝 III
目錄 IV
表目錄 VII
圖目錄 VIII
第一章緒論 - 1 -
1.1 研究動機與目的 - 1 -
1.2 論文架構 - 1 -
第二章文獻回顧 - 3 -
第三章理論方法 - 7 -
3.1 理論背景 - 7 -
3.1.1 梁元素與自由度的關係 - 7 -
3.1.2 狀態空間方程式 - 14 -
3.1.3 Tikhonov正規化法 - 16 -
3.1.4 正規化參數 - 18 -
3.2 動態反算問題之程序化 - 20 -
3.2.1 前言 - 20 -
3.2.2 Bellman動態規劃 - 20 -
3.3 模態法 - 29 -
第四章數值模擬與分析 - 32 -
4.1 二維簡支梁模擬 - 32 -
4.1.1 梁構件模型 - 32 -
4.1.2 梁元素參數 - 34 -
4.1.3 移動力加載形式 - 36 -
4.1.4 動態載重之識別結果 - 36 -
4.2 三維Grid梁元素之簡支梁模擬 - 43 -
4.2.1 移動力量加載形式 - 44 -
4.2.2 不同應變計數量之識別結果 - 45 -
4.2.3 不同速度之識別結果比較 - 61 -
第五章三鶯大橋動載實驗 - 70 -
5.1 試驗位置 - 70 -
5.2 實驗儀器 - 72 -
5.3 試驗載重車型式 - 73 -
5.4 載重車作用位置 - 73 -
5.5 大梁應變位置 - 74 -
5.6 識別結果 - 76 -
第六章結論與建議 - 81 -
6.1 結論 - 81 -
6.2 建議 - 82 -
參考文獻 - 83 -
附錄 A - 86 -
附錄 B - 93 -

參考文獻

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指導教授

王仲宇

審核日期

2014-7-31

推文