非線性阻尼應用及阻尼最佳化分配研究

Abstract

近年來黏性阻尼器(Viscous Damper)被廣泛應用於建築結構，作為被動消能元件，然而現行設計規範，並未針對阻尼器配置方式有具體之建議與規定。然而阻尼器配置於不同樓層，卻影響了各建築結構受地震力後之反應，故選擇一有效之分配法，將可提升抗震效益。 本研究針對於目前實務上較常使用之非線性阻尼器進行比較，首先針對於單自由度之非線性阻尼進行驗證，從非線性阻尼比估計公式可推得各模型之非線性阻尼係數，然而相較線性之阻尼比估計，穩態位移亦是參數之一，為確保於地震此非穩態之力量下單自由度非線性阻尼仍可保守且有效地發揮阻尼效益，將反應譜全部及部份阻尼比換為非線性阻尼，並利用不同週期之單自由度模型，進行非線性反應譜繪製，針對各非線性產生之譜加速度進行分析，以確保使用非線性阻尼可發揮與線性阻尼相當之折減效益。 為討論各阻尼器分配法之成效，利用現有之「直接分配法」三種及「動力分析分配法」進行討論，並討論台北一區、台北二區、台北三區及台中西屯第一類地盤四種區域，利用四種剪力構架用以比較各種模型阻尼分配法之適用，並利用不同之非線性指數，以比較非線性情況，為使各模型皆在相同之基準下比較，使各模型於均勻配置法線性及非線性阻尼器下具有相同外加阻尼比。 比較不同分配法時，利用各分配法與均勻分配法之最大層間位移角之差值，作為折減指標，以期望各分配法優於均勻分配法；比較非線性與線性阻尼器時，利用各分配法於線性與於非線性之最大層間位移角之差值，以期望非線性阻尼器優於線性阻尼器；再針對線性與非線性阻尼模型於設計地震力與中小型地震力水平總橫力進行比較，以討論非線性阻尼反應譜與實際動力歷時非線性阻尼器多自由度之模型產生之水平總橫力折減效益。

In recent years, viscous dampers have been widely used in building structures as passive energy-dissipation devices. However, the current design codes do not prescribe specific recommendations and regulations for damper allocation. Although dampers are placed on different floors, the response of each building structure to seismic forces is different. Therefore, choosing an effective damping distribution method will improve the seismic resistance. This study compares the various nonlinear dampers that are widely used in practice. First, the single-degree-of-freedom nonlinear damping of these dampers is verified. By using the formula for estimating the nonlinear damping ratio, the nonlinear damping coefficients of each damping model can be determined. To ensure that the single-degree-of-freedom nonlinear damping can conservatively and effectively exert damping benefits under the non-steady-state forces of earthquakes, all or a part of the response spectrum of the damping ratio is changed from linear to nonlinear damping, single-degree-of-freedom models with different periods are used to draw the nonlinear response spectrum, and the spectral acceleration generated by each nonlinearity is analyzed to ensure that the nonlinear dampers can effectively serve as equivalents to linear dampers. To discuss the effectiveness of each damping-distribution methods, three types of existing 'direct distribution methods' and two types of 'dynamic analysis distribution methods' are considered. Moreover, the first-class sites Taipei I, Taipei II, and Taipei III, and the Class I Taichung Xitun site are considered to compare the application of various damping-distribution models, and different nonlinear exponents are used to compare various nonlinear conditions. All of the models are compared against the same benchmark to ensure they have the same external damping ratio with linear and nonlinear dampers in the uniform distribution method. To compare different distribution methods, the difference between the maximum story drift ratio of each distribution method and that of the uniform distribution method was used to demonstrate that each of the distribution methods was superior to the uniform distribution method. To compare the nonlinear and linear dampers, each of the distribution methods was used based on the difference in the maximum story drift ratio between the linear and nonlinear dampers, to demonstrate that the nonlinear dampers were superior to the linear dampers. Then, small and medium seismic forces were applied to compare the design forces of the linear and nonlinear damping models with the total horizontal force.