以簡化方法分析具非比例阻尼之平面不對稱建築

Simplified Seismic Analyses of Non-Proportionally Damped Asymmetric-Plan Buildings

劉子豪(Tze-How Liu)

指導教授 ： 蔡克銓

國立臺灣大學/工學院/土木工程學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.00526

摘要

台灣是由歐亞大陸板塊與菲律賓海板塊相互碰撞擠壓而成，每年會有15000至18000個大大小小的地震，因此在台灣設計建築結構時地震力是最重要的考量因素之一。現今社會越來越多造型獨特的建築，這些外觀特殊的建築往往會有平面不對稱的情形，受震時平移及旋轉的變形往往同時發生，角落位移有可能比質心位移還大甚多，且以傳統的靜力分析方法無法準確地預測其受震反應，因此常須採動力分析方得以檢核其耐震性能。隨著都市人口密度增加，高樓層建築也越來越多，許多高層建築加裝液態黏滯性阻尼器來增強其制震能力。本研究探討簡化的動力分析方法以計算加裝液態黏滯性阻尼器的平面不對稱建築之受震反應。以便用於初步設計、大量分析以及參數研究。
本研究主要分為兩個部分：一為具線性液態黏滯性阻尼器之非彈性平面不對稱建築的簡化分析，另一為具非線性液態黏滯性阻尼器之彈性平面不對稱建築的簡化分析。兩個部分均採用模態疊加法來計算結構之受震反應。第一部分，本研究利用動力分析軟體建立振態桿狀模型並設置雙線性參數以探討結構受震進入非彈性之反應。再比較本研究提出之簡化方法與傳統單自由度模態運動方程式運算結果之準確度。而第二部分使用數學軟體藉Newmark-β法計算具有外加非線性阻尼器的多自由度模態運動方程式。針對非線性外加阻尼項的計算，本文提出預測修正法以及等效阻尼係數法兩種簡化方法。預測修正法在分析過程中，預估了非線性項次的速度，並且修正上一步計算產生的不平衡力。等效阻尼係數法於Newmark-β法每一個計算步距計算每支非線性阻尼器對應於線性阻尼器之等效阻尼係數，再以此係數建置新的阻尼矩陣，進而求得下一步的結構反應。
上述兩個部份的研究均以PISA3D動力分析軟體建置有限元素模型之受震反應作為精確解比較其準確度。本研究第一部份中提出的簡化方法，在多數案例中誤差值均較傳統單自由度方法小，縱使有些分析案例峰值準確度沒有明顯優於或甚至劣於傳統簡化方法，但本研究提出之簡化方法預估之結構動態反應趨勢與有限元素模型分析得到的結果較相近。第二個部份之分析案例中，在阻尼指數 的情況，兩種簡化方法均有良好的表現，隨著 值增大，兩種簡化方法準確度均劇烈下滑。另外預測修正法於 的分析案例中受震反應隨著時間衰減的趨勢比較緩慢，等效阻尼係數法預測之受震反應隨著時間衰減的情形有比較精確的表現。兩種簡化方法均能有效地節省分析所需時間，等效阻尼係數法耗時約為有限元素法之16%，預測修正法耗時只為有限元素法之8%。

關鍵字

振態分析 ； 非比例阻尼 ； 非線性阻尼器 ； 平面不對稱 ； 反應歷時分析

並列摘要

Seismic loading is one of the most important load cases while designing buildings in Taiwan. There are more and more high-rise buildings with grotesque appearance assembled with fluid viscous dampers in order to enhance the ability of energy dissipation. The response of these special-shaped buildings, which usually are asymmetric-plan structures, excited by bi-directional ground motions can’t be evaluated accurately using traditional static analysis procedures. This research proposes simplified seismic analysis methods for non-proportionally damped asymmetric-plan buildings. Simplified methods could be effectively applied to preliminary design, parametric study, and extensive analyses to save computation time.
This study includes two parts: 1) simplified seismic analyses of inelastic asymmetric-plan buildings with linear viscous dampers, and 2) simplified seismic analyses of elastic asymmetric-plan buildings with nonlinear viscous dampers. In the first part, the multi-degree-of-freedom (MDOF) modal stick with supplemental damping is constructed using a general purpose nonlinear dynamic response analysis program PISA3D. The stated MDOF modal sticks, instead of the conventional single-degree-of-freedom (SDOF) modal sticks, are used in the uncoupled modal response history analysis procedures. In the second part, two simplified methods, including the predictor-corrector method (PC) and the effective-damping-coefficient method (EDC), are proposed to solve the MDOF modal equations of motion. The PC method first predicts the velocity of the nonlinear term, then corrects the unbalanced force at the next time step. The EDC method computes the damping coefficient of the equivalent linear viscous damper corresponding to each nonlinear viscous damper at each time step. The MDOF modal equations of motion resulting from the equivalent linear viscous dampers instead of the nonlinear viscous dampers are solved by using step-by-step integration method. The Newmark-βmethod are implemented by using the MATLAB program.
In this study, the seismic responses computed from the complete finite element models of buildings are considered as the exact solution. Most of the seismic responses obtained from the proposed simplified method in the first part of this study are more accurate than those obtained from the other conventional simplified method. In addition, the proposed simplified method captures the trend of dynamic responses much better than the other simplified method. In the second part of this study, both the PC and EDC methods perform satisfactorily when the damping exponent η is less than or equal to one. When η is more than one, the accuracies of the estimated responses resulting from both methods decrease significantly. The EDC method is better than the PC method in capturing the decayed responses occurred after the main excitation of earthquakes. These two simplified methods significantly improve the computation efficiency. The computation times by using the EDC and PC methods are about 16% and 8%, respectively, of that cost by analyzing the complete finite element models of buildings.

並列關鍵字

modal analysis ； supplemental damping ； nonlinear damper ； asymmetric-plan building ； response history analysis

參考文獻

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