以磁流變阻尼器控制斜張鋼纜之振動：理論與實驗探討

Abstract

斜張鋼纜作為斜張橋重要的構件，因其低阻尼的特性易受外力影響引起振動，造成斜張橋的不穩定。為解決這類可能造成災害的振動問題，有人提出以安裝黏滯性阻尼器增加斜張鋼纜阻尼比的方式減少鋼纜振動，但黏滯性阻尼器因安裝位置靠近下方錨碇端的關係通常只能增加少量的阻尼比。隨著斜張橋跨度的增加，斜張鋼纜的長度也愈來愈長，黏滯性阻尼器所能提供的阻尼比也會相對減少。因此近年來，有學者提出以可變強度的磁流變阻尼器代替黏滯性阻尼器可以有效降低斜張鋼纜的振動。 本研究實際架設一根長13.5公尺並施加預力的斜張鋼纜，以安裝磁流變阻尼器配合半主動控制理論抑制斜張鋼纜受正弦波外力造成的振動。因為數值模擬與控制實驗的需要，以有限元素分析軟體ABAQUS得到簡化後的斜張鋼纜數值模型；並對使用的磁流變阻尼器進行性能測試實驗再利用Bouc-Wen Model理論模擬磁流變阻尼器的非線性行為。 實驗的控制策略採用以二個加速度訊號和阻尼器力量作為回饋的LQG理論及僅使用阻尼器的位移和力量為回饋的分散式滑動模式控制理論(DSMC)。本研究實驗了一系列的測試項目，包含未安裝磁流變阻尼器、磁流變阻尼器輸入固定電壓及以半主動控制理論決定輸入電壓等測試，實驗證明磁流變阻尼器配合半主動控制理論可以有效抑制斜張鋼纜的振動，也證明了磁流變阻尼器在斜張鋼纜控制系統中的彈性與適用性。

As a critical member of cable-stayed bridges, stay cables are prone to vibration due to their low inherent damping characteristics, and this characteristic will even make cable-stayed bridges unstable. To solve these hazardous vibration problems, various measures have been developed. One of the effective ways is to install viscous dampers to reduce such vibration. However, only minimal damping value can be added because the attachment point is close to the lower anchorage. With the span of cable-stayed bridge and the length of stay cable become longer, viscous damper may not provide sufficient damping value to reduce the cable vibration. Therefore, researchers have proposed the semi-active MR-dampers to reduce cable motion as an alternative to the viscous dampers. In this study, a 13.5 m inclined cable has been setup, and a semi-active MR-damper is installed to reduce cable motion which is caused by a sinusoidal force. For the experiment and numerical simulation, the system matrices of the simplified cable model are generated from ABAQUS. The Bouc-Wen Model is used to simulate the non-liner behavior of the MR-damper using the performance test. Two control theories are verified experimentally in this study: one is employing LQG control using two acceleration signals and the damper force as feedback and the other is using Decentralized Sliding Mode Control (DSMC) theory with only local measurement as feedback. A series test is carried out to investigate the control performance which includes: unattached MR-damper, passive-on MR-damper and semi-active MR-damper. Through the results from the experimental test, the semi-active cable vibration control system with MR damper can reduce the cable motion well under different kinds of excitations.