本文旨在研究單自由度非線性分數階微分系統。將分數階阻尼係數與非線性係數視為主要變數，藉由改變主要變數觀察系統反應之變化。將兩種不同方法分別為數值分析法與近似解析法交互比較，據以分析參數正規化下之振幅的反應及差異。本研究針對合理參數組合範圍進行探討並繪製振幅頻譜圖，分析結果顯示用數值分析法在低頻時會產生內嵌高頻波，而用近似解析法則能分析出比數值分析法更大的峰值，並在達到峰值後有內凹之現象。

This study mainly discusses a steady-state response of nonlinear fractional damping system. In order to observe different response in system by changing some variables, fractional damping coefficient and nonlinear coefficient are regarded as mainly variables. To analyze response and difference of amplitude spectra with parameter normalized, the study uses two different ways like numerical method and approximate analysis method. This project discusses with reasonable range of parameters, and reveals the amplitude spectra. When using numerical method, some results of analysis show an embedded high frequency wave at low frequency ratio. Moreover, when using approximate analysis method, it can indicates higher amplitude than numerical method. In addition, there is a concave after the peak.

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