本文旨在研究分數微分用於動力系統之分析。本研究根據Riemann-Liouville分數階微分之定義為基礎，引入Newmark法分析動力系統之時間歷時反應；研究進一步以單自由度動力系統安裝分數階微分阻尼，並輸入不同之阻尼係數與分數階微分值，觀察自由震動之反應；最後將此動力系統輸入台灣921集集地震資料，分析系統之反應與差異。研究結果顯示，隨著分數階微分值上升，產生一部分勁度遞轉成阻尼的趨勢，而隨著阻尼係數上升，此種趨勢將更為明顯；另外，利用反應譜分析發現，隨著系統的自然週期越大，使用分數微分與整數微分間的差異也越大。

This paper aims to study the fractional derivatives used in analysis of power system. This study is based on the definition of Riemann-Liouville fractional derivatives as the basis and introduced Newmark method to analyze the response of time history of dynamical systems.
The study further use the dynamic system with a single degree of freedom to input different value of damping and fractional differential, and observe the response of free vibration;Finally, to analyze the response and differences of power system installed fractional damping system through 921 Taiwan Chi-Chi earthquake data.
The results showed a rising value of fractional differential produce the trend transferred stiffness to damping of structure, with the increase in damping coefficient, and this trend will become more obvious.
In addition, the use of response spectrum analysis found that the greater natural period, the more difference between the use of fractional and integer differential.

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