尤拉梁外力的閉合係數展開識別法

A closed-form coefficients expansion method for recovering spatial-dependent load on the Euler-Bernoulli beam equation

黃柏彰(Po-Chang Huang)

指導教授 ： 劉進賢 ； 鍾立來

國立臺灣大學/工學院/土木工程學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201703569

摘要

在土木工程議題中，橋梁的振動是非常重要的一塊領域，而橋梁又可以理想地簡化為尤拉梁進行分析。在正算尤拉梁問題時處理手段有許多種，而當處理欲反求外力的尤拉梁問題(源識別)時，計算量與困難度將會增加許多。本文使用邊界積分方程法(BIEM)，搭配伴隨Trefftz測試函數之概念，引入振態的概念做為基底，並發展出新的閉合係數展開識別法。由於過程之中沒有重積分及大尺度的反矩陣運算，且求出之解為閉合解，因此能夠得到誤差小、精度高的結果。論文中將以數值算例，實際求解尤拉梁的外力反算問題，其中包含各種不同邊界條件的梁以及其對應之振態做為基底，另外並加入噪音進行分析，最後與精確解進行比對，分析數值結果。

關鍵字

邊界積分方程法 ； 尤拉梁 ； 伴隨Trefftz測試函數 ； 廣義格林第二恆等式 ； 自我伴隨運算子 ； 源識別問題 ； 閉合係數展開識別法

並列摘要

In the field of Civil engineering, the forced vibration of a bridge is a big issue. When discussing the behavior of a bridge, we can apply the Euler-Bernoulli beam theory to analyze it simply. There are several methods to analyze the Euler-Bernoulli beam equation under an external force; however, without knowing the external force, it becomes an inverse source problem which is much more complicated.In this thesis, we adopt the boundary integral equation method (BIEM) with the mode shapes as adjoint test functions. Then, we can develop a non-iterative method to recover a space-dependent load on the Euler-Bernoulli beam named closed-form expansion coefficients method. Finally ,we give some numerical examples to demonstrate the efficiency and accuracy of the proposed new method.

並列關鍵字

Boundary Integral Equation Method (BIEM) ； Euler-Bernoulli Beam ； Adjoint Trefftz Test Function ； Closed-Form Expansion Coefficients Method

參考文獻

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