本論文研究簡化土壤與五層抗彎矩構架互制系統在水平地震作用下的動態行為，以白訊、高斯函數及窗函數之能譜密度函數地震輸入，在頻率域進行隨機振動分析。
研究結果顯示，當輸入地表振動的能量譜密度函數PSD為白訊時，比較簡化模式與實際模式的反應，五樓頂加速度反應PSD及標準差最大誤差均不超過10%。在輸入地表振動PSD為高斯函數時，加速度反應PSD與標準差最大誤差均不超過8%。因此，簡化模式應可適當模擬土壤真實狀況，應用於土壤結構互制系統之隨機振動分析。當輸入地表振動能量譜密度函數為窗函數時，若輸入運動的顯著頻率接近系統共振頻率，簡化模式可有效適用，但顯著頻率遠離系統共振頻率時，則簡化模式需做適當調整使用。
此外，比較簡化模式與實際模式，五樓頂加速度標準差的誤差隨樓層質量比線性減少；五樓頂加速度標準差將隨著樓層勁度比線性增加。未來簡化模式的改良可據此發現做適當調整。

In this thesis, the dynamic behavior of a simplified soil and a five-story MRF interaction system under horizontal earthquake is studied. The Power Spectral Density(PSD) functions of the seismic input under the form of white noise, Gaussian function and window function are used to perform random vibration analysis in the frequency domain.
The results show that when the PSD of the input surface vibration is a white noise, the response between the simplified system and the real system is well compared, and the maximum errors of the PSD and the standard deviation of the acceleration response at the top of the building are all less than 10%. When the input surface vibration PSD is a Gaussian function, the maximum errors of the acceleration response PSD and the standard deviation are all less than 8%. Therefore, the simplified system should be able to properly simulate the true state of the soil and be applied to the random vibration analysis of the soil structure interaction system. When the PSD of the input surface vibration is a window function, if the main frequency of the input motion is close to the system resonance frequency, the simplified system can be effectively applied, but when the main frequency is far away from the system resonance frequency, the simplified system needs to be properly adjusted.
In addition, comparing the simplified system with the real system, the error of the standard deviation of the acceleration response at the top of the building decreases linearly with the floor mass ratio and increases linearly with the floor stiffness ratio. Therefore, improvements to future simplified systems can be adjusted accordingly.

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