即時複合實驗(Real-time hybrid testing，RTHT)係一種先進的實驗技術，已被多數的學者驗證過。即時複合實驗原理係將一結構系統分為主結構與子結構，其中主結構係用數值模型模擬其動力反應，而子結構則以油壓制動器進行實驗。該油壓制動器模擬主結構位移反應並將力量施加於子結構上，同時將荷重計量測之子結構反力傳至電腦，該電腦再利用回饋之子結構反力量測值與數值積分方法計算下一步主結構位移反應。故即時複合實驗可模擬結構系統受到地震力作用下之動態反應。然而對於具摩擦特性之子結構則難以使用即時複合實驗模擬其動力反應，因受地震力作用下之摩擦元件動力行為(滑動或黏著)係與結構之加速度相關。為能於具摩擦特性子結構之即時複合實驗中模擬主結構加速度，本文提出振動台即時複合實驗(Real-time hybrid testing with a shaking table，RTHT-ST)。在振動台即時複合實驗中，子結構係安裝於振動台上並以振動台模擬主結構之動力反應。為驗證振動台即時複合實驗之可行性，本文提出一系列的四種具摩擦特性子結構之振動台即時複合實驗，並將複合實驗結果與振動台實驗結果進行比較。本文提出之四種具摩擦特性子結構分別為1. 槓桿式勁度可控質量阻尼器(Leverage-type stiffness controllable mass damper，LSCMD)，其勁度可隨槓桿支點位移變化而調整；2. 壓電式摩擦可控質量阻尼器(Piezoelectric friction controllable mass damper，PFCMD)，其摩擦力可隨壓電致動器的輸入電壓變化而調整；3. 多項式摩擦單擺支承樓板隔震系統Polynomial friction pendulum isolators floor isolation system，PFPI-FIS)，其回復力及摩擦係數分別可隨隔震位移與隔震速度變化而變化；4. 壓電式智慧樓板隔震系統(Piezoelectric smart floor isolation system，PSFIS)，其摩擦力可隨壓電致動器的輸入電壓變化而調整。再者，因控制延遲時間可能對振動台即時複合實驗造成影響，故本文亦提出一遞迴最小平方法(Recursive least squares，RLS)估測之反轉換補償法(Inverse compensation method，ICM)。為評估振動台即時複合實驗結果之可靠性，本文提出兩種性能指標。第一種為能量誤差指標，該指標係按照前人研究方法計算。第二種為均方根能量誤差(Root-mean-squares energy error，REE)指標，該指標可計算即時複合實驗之總誤差、控制誤差與模型誤差。振動台實驗與即時複合實驗結果之比較顯示，振動台即時複合實驗可模擬受地震力作用下之主結構與具摩擦特性子結構之動力反應，且本文提出之時間延遲補償方法亦可改善振動台系統之控制效能。本文提出之效能指標可顯示振動台即時複合實驗結果之可靠性。此外，以迴歸分析與均方根能量誤差值計算得到之迴歸方程式可以均方根能量誤差之控制誤差與模型誤差預測總誤差。

Real-time hybrid testing (RTHT) is a novel experimental technique that is validated by many researchers. RTHT divides a structural system into a primary structure whose dynamic responses can be described by a numerical model, and a substructure which is experimentally tested with an actuator. The actuator simulates the displacement of the primary structure and applies force on the substructure, while the measured reaction force of the substructure is transmitted to the computer that determines the next step structural displacement by using the feedback reaction force and an integration algorithm. Therefore, the dynamic responses of the structural system subjected to seismic excitations can be simulated by using RTHT. However, the dynamic responses of a substructure with a friction component are hard to be simulated in RTHT because the dynamic behavior (slipping or sticking) of a friction element subjected to seismic forces relates with structural acceleration. In order to consider structural acceleration for a substructure with a friction component in RTHT, real-time hybrid testing with a shaking table (RTHT-ST) is proposed in this thesis. In RTHT-ST, a substructure is installed on a shaking table which simulates the dynamic responses of the primary structure. To verify the feasibility of RTHT-ST, a series of RTHT-ST tests for substructures with four types of friction components is conducted and the experimental results of the RTHT-ST are compared to those of shaking table testing (STT). The four substructures are: 1. a leverage-type stiffness controllable mass damper (LSCMD) whose stiffness can be adjusted by varying the pivot displacement of a leverage; 2. a piezoelectric friction controllable mass damper (PFCMD) whose friction can be adjusted by varying the input voltage of the piezoelectric actuator; 3. a polynomial friction pendulum isolators floor isolation system (PFPI-FIS) whose restoring force varies with isolation displacement and friction coefficient varies with sliding velocity; 4. a piezoelectric smart floor isolation system (PSFIS) whose friction can be adjusted by varying the input voltage of the piezoelectric actuator. Moreover, an inverse compensation method with recursive least squares (RLS) estimation is proposed since the control delay time could be an issue in RTHT-ST. To evaluate the reliability of the RTHT-ST, two performance indices are proposed. The first index, called energy error index, is based on the previous study. The other index, called root-mean-squares energy error (REE) index, considers total (control and modeling) errors between RTHT-ST and STT. The comparisons between the experimental results of the RTHT-ST and those of the STT demonstrate that the dynamic behavior of the primary structure with four substructures subjected to seismic excitations can be simulated by using RTHT-ST, and the proposed compensation method improves the control performance of the shaking table system. The proposed performance indices indicate the reliability of the RTHT-ST experimental results. In addition, the regression equation which are computed by using regression analysis and the REE index values can predict the total error of the RTHT-ST tests by using the control and modeling errors.

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