直接更新法應用於結構模型之更新

Abstract

結構模型數值分析結果與實驗量測結果相較，經常會發現兩者之間有明顯的差異。針對此一問題，本文旨在發展一套簡便的有限元素模型更新方法，即直接更新法，利用質量或勁度矩陣和模態間的正交關係，來更新結構模型的理論質量和勁度矩陣。首先假設第一模態資料可被量測得到，利用模態矩陣取代模態向量，可推導出質量和勁度矩陣的更新式。接著，假設前幾個模態的資料可被量測得到，前述單一模態更新法可被延伸至多重模態更新，可採用兩種不同的更新方式，即依序更新各個模態，或同時更新前幾個模態。不論將上述的直接更新法應用於剪力屋架、懸臂梁、連續橋樑或是拱狀結構，皆可以發現更新後結構模型所預測的振動頻率，和量測得到的前幾個模態的振動頻率是吻合的，但剩下未能得到量測資料的高模態振動頻率，則大致不受影響。最後，將本文提出的直接更新法和Lin等人(1995)提出的改善逆特徵敏感度矩陣法(IIEM)做比較，可發現本文提出的有限元素模型直接更新法，在計算過程上較簡便，在工程應用上也較適合。由於本文發展的有限元素模型更新法，僅需簡單的計算過程，相較於其他已存在的更新方法，可以更有效的應用落實於土木工程上。

Discrepancies always exist between the dynamic properties predicted by a finite element model and those measured directly from the structure. In this study, a direct updating method based on the orthogonality constraints is proposed for updating the mass and stiffness matrices of the structure first using a single set of modal data. This method hinges on replacement of the modal vector of concern by the modal matrix in computing the correction matrices to solve the problem of insufficient known conditions. Such a method is then extended to update the structural model for each of the first few sets of modal data that are experimentally made available. Two kinds of updating procedures are proposed, one is to conduct the model updating in a mode-by-mode manner and the other is in a simultaneous manner. In the numerical studies, it was demonstrated that for buildings of the shear type, the cantilever beam, continuous bridges and domes, the natural frequencies predicted by the updated model agree well with the measured ones for those modes that are experimentally made available, while the remaining modes remain basically untouched. In the end, a comparative study is performed for the proposed direct model updating method and the improved inverse eigensenstivity method (IIEM) proposed by Lin et al. (1995) for updating the mass and stiffness matrices of a structure based on the measured modal data. From the comparison study, it is demonstrated that the direct updating method presented herein is superior and more suitable for engineering applications. Since the proposed approach is simple, accurate and robust, it should be favored by engineers for practical applications.