本文針對短記憶理論應用於具分數階微分動力系統之可行性執行分析。為配合短記憶理論對分數階微分之短記憶處理，本研究根據Riemann-Liouville分數階微分之定義，並以Newmark法作為數值解析工具。本文以單自由度系統之時間歷時反應作為比較基礎，據以觀察在不同分數階微分值下短記憶長度與全程記憶處理之反應差異。本文也利用台灣921集集地震資料為系統之動力輸入，分析短記憶理論用於地震反應譜分析之可行性。研究結果顯示，在較高分數階微分值之情形下，利用短記憶長度仍可獲致合理之精準值。

This study presents an analysis of dynamical systems with fractional derivatives using the short memory principle. The study is based on the Remann-Liouville definition for the fractional derivative and the Newmark method is adopted to evaluate the responses. In this work, the response time history of a single-degree-of-freedom system is used as a comparison basis. The effects of different memory length and different fractional orders are identified by comparing the response differences between the short and full memory analyses. The feasibility of applying the short memory principle for response spectral analysis is also investigated where the 921 Taiwan Chi-Chi earthquake data are used as inputs. Study results show that under high fractional order, reasonable response accuracy can still be obtained when the short memory principle is applied.

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