以正規化邊界積分法分析非線性液體沖激行為及其在諧調液體阻尼器之應用

Study on Nonlinear-Liquid-Sloshing Behavior and Its Application on Tuned-Liquid Damper by Regularized Boundary Integral Method

曹文懷(Wen-Huai Tsao)

指導教授 ： 陳永祥

共同指導教授 ： 黃維信

國立臺灣大學/工學院/土木工程學研究所/博士(2018年)

https://doi.org/10.6342/NTU201800148

摘要

本文以正規化邊界積分法(regularized boundary integral method, RBIM)模擬液體於二維矩形水槽及三維圓柱形水槽內之非線性沖激(sloshing)行為，以及諧調液體阻尼器(tuned liquid damper, TLD)之應用。沖激問題可視為勢流場(potential flow)中之混和型邊界值問題(mixed type boundary value problem)，並由正規化邊界積分法求解之。因利用消除補償技巧(subtracting and adding-back technique)，於邊界積分式中減去特定積分式，再以等價之積分式補償，以消除奇異積分(singular integral)及近鄰奇異積分(nearly singular integral)，故稱正規化。相較於傳統邊界元素法(boundary element method, BEM)，正規化邊界積分法較為準確、穩定及可靠，並透過直接的演算法達成高效率計算。
求得邊界上未知物理量後，利用拉格朗日(Lagragian)座標描述法追蹤自由液面運動，再由伯努力方程式(Bernoulli equation)求得槽壁上的壓力分佈，其槽底合力可視為施加於結構之外力，以此模擬液體與結構的互制行為(liquid-structure interaction)。最後藉由狀態空間法(state-space method)，求解液體與結構互制之運動方程式，分析諧調液體阻尼器的動力特徵與減震效果。
為模擬液體阻尼器之消能機制，自由液面之動力邊界條件增加一項與速度相關之線性阻尼，於此稱為人工阻尼，其人工阻尼係數(artificial damping coefficient)係根據試驗求得。以單自由度(Single-degree-of-freedom, SDOF)之單擺結構為例，參考附加諧調液體阻尼器之主結構位移的頻率響應函數(frequency response function)，追求設計參數的最佳化。另外，使用等效諧調質量阻尼器模擬，驗證數值方法的適用性，並討論與諧調質量阻尼器(tuned mass damper, TMD)之間的差異與優劣。最後，將研究成果應用於台北101，展現諧調液體阻尼器的經濟性與實用性。本文所使用的理論基礎與數值方法，經過實驗驗證，顯示了良好的準確性、穩定性、可靠性及實用性。

關鍵字

非線性沖激行為 ； 諧調液體阻尼器 ； 液體與結構互制作用 ； 勢流理論 ； 正規化邊界積分法 ； 人工阻尼係數 ； 等效諧調質量阻尼器

並列摘要

The nonlinear sloshing simulation by the regularized boundary integral method (BIM) and its application on two-dimensional (2D) rectangular and three-dimensional (3D) cylindrical tuned liquid dampers (TLD) are studied. Based on potential flow theory, the sloshing problems can be referred to the boundary value problem (BVP) with mixed type boundary condition, which can be solved by RBIM. By using the subtracting and adding-back technique, several identities are utilized to eliminate the singularities or near-singularities of surface integrals, and then the equivalent integrals are compensated to obtain the regularized boundary integral equation (BIE), therefore it is called as regularization procedure. Compared to traditional boundary element method (BEM), it is not only more accurate and stable to analyze the sloshing problems, but also more efficient due to the simpler algorithm.
When liquid is excited, the free surface motion can be acquired by the Taylor series expansion (TSE) through the Lagrangian description after solving the physical unknowns. The resultant force obtained by summing the pressure on walls from Bernoulli equation, can be regarded as an external force applied to the structure. Therefore the interaction model between liquid and structure can be established to analyze the dynamic responses of the structure and TLD by the state space method.
In order to simulate the damping mechanism of TLD, the linear proportional damping term, which is called as artificial damping, is introduced to the dynamic boundary condition on the free surface. Several small-scaled model tests, including harmonic and earthquake excitations, on a shaking table are carried out to verify the artificial damping coefficient for fresh-water TLD or TLD equipped with vertical screens. Therefore the dynamic characteristic of TLD and the optimal design parameter could be drawn by comparing the frequency responses of a single-degree-of-freedom (SDOF) system. On the other hand, the simple equivalent TLD model is employed and then the results by both models are compared with those of tuned mass damper (TMD). At last, the performances of TLD on Taipei 101 are demonstrated to show its advantages of economy and applicability. The fundamental theory and numerical method used in this study shows good agreement with the experimental results, and present the excellent accuracy, stability, practicality and reliability.

並列關鍵字

Nonlinear sloshing behavior ； Tuned liquid damper ； Liquid and structure interaction ； Potential flows ； Regularized boundary integral method ； Artificial damping coefficient ； Equivalent mass damper

參考文獻

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