纜索─阻尼器─繫索系統之動力特性研究

Investigation on Dynamic Characteristics of Cable-Damper-Crosstie Systems

游維新(Wei-Hsin Yu)

指導教授 ： 劉明怡 ； 黃仲偉

中原大學/工學院/土木工程研究所/碩士(2018年)

https://doi.org/10.6840/cycu201800879

摘要

本研究嘗試將線性黏性阻尼器與繫索兩種元件同時應用於繃緊纜索，使用有限元素法探討「纜索─阻尼器─繫索系統」的動力特性，並決定「阻尼器─繫索」之最佳參數。係以自由振動為基礎，利用複數振態分析計算系統單一振態參數，包含自然頻率、阻尼頻率、阻尼比與振動型態，並建立阻尼比、阻尼器阻尼係數和繫索勁度係數的關係曲面，在設定系統阻尼比極大化為目標函數的前提下，可決定系統最佳阻尼比與對應之阻尼器最佳阻尼係數和繫索最佳勁度係數。此外，考慮未裝設阻尼器之纜索，在高斯白噪音激振之條件下，利用經驗模態分解法將系統位移歷時拆解成各個振態位移歷時之本徵模函數，並計算其均方根值，可推估其權重因數；接著，考慮裝設阻尼器之纜索，計算系統各個振態之阻尼比；最後，結合各個振態的權重因數與阻尼比，即可得「單纜索─阻尼器系統」之等效阻尼比建議公式。在設定系統等效阻尼比極大化為目標函數的前提下，可決定將各個振態動力參數組合後，系統等效最佳阻尼比和對應之阻尼器最佳阻尼係數。經由本研究成果可全面地瞭解「纜索─阻尼器─繫索系統」之力學機制，並合理地決定「阻尼器─繫索」之最佳參數。

關鍵字

線性黏性阻尼器 ； 繫索 ； 繃緊纜索 ； 複數振態分析 ； 等效阻尼比

並列摘要

The objective of this study is to fully understand the dynamic characteristics of taut cables with both attached linear viscous dampers and crossties as well as to accurately determine the optimal parameters of the dampers and crossties. Based on the free vibration theory, the complex modal analysis is adopted to calculate the natural frequency, damped frequency, damping ratio, mode shape, and the surface of damping ratio, damper damping and crosstie stiffness for each mode of the "cable-damper-crosstie system". The mentioned surface can be provided to determine the optimal damping ratio, and the corresponding optimal damper damping and optimal crosstie stiffness for each mode of such system. Furthermore, for the "single cable-damper system" under Gaussian white noise excitations, a formula is proposed to determine the optimal equivalent damping ratio by combing the weight factor and damping ratio for each mode of such system. Compared to the optimal damping ratio for a certain mode, the optimal equivalent damping ratio containing the contributions from a number of dominant modes is a more rational index for reducing cable vibrations.

並列關鍵字

Linear Viscous Damper ； Crosstie ； Taut Cable ； Complex Modal Analysis ； Equivalent Damping Ratio

參考文獻

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