本研究針對結構物自然頻率和阻尼比的不確定性進行探討，特別是在參數具有已知上下限但確定值不明的情況下。系統分析採用非概率方法來描述這種不確定性，並比較取點分析、參數擾動方法和正交多項式方法對結構反應的影響。
研究結果顯示，在對阻尼比的不確定性進行估算時，這三種方法均表現出很高的精確度。這意味著，不論是採用取點分析、參數擾動法還是正交多項式法，都能可靠地處理阻尼比的不確定性情況。
在對自然頻率的不確定性進行估算時，結果顯示在大範圍不確定性情況下，取點分析提供了最佳的位移範圍估算；而在小範圍不確定性情況下，參數擾動法能迅速給出結果，而正交多項式法則提供了最高的精確度。本研究有助於更好地理解不同分析方法對結構反應的影響，並為選擇最適合特定工程問題的方法提供指引。

This study investigates the uncertainty associated with the natural frequencies and damping ratios of structures, particularly when the parameters have known upper and lower bounds but unknown precise values. Non-probabilistic methods are employed to characterize this uncertainty, and the effects of point sampling analysis, parameter perturbation methods, and orthogonal polynomial methods on structural response are compared.
The research findings demonstrate a high level of accuracy for all three methods when estimating the uncertainty in damping ratios. This suggests that whether using point sampling analysis, parameter perturbation methods, or orthogonal polynomial methods, the uncertainty in damping ratios can be reliably addressed.
Regarding the estimation of uncertainty in natural frequencies, the results indicate that point sampling analysis provides the best estimate of displacement range in cases of large-range uncertainty. For small-range uncertainty, parameter perturbation methods offer quick results, while orthogonal polynomial methods provide the highest level of precision. This study contributes to a better understanding of the impact of different analysis methods on structural response and provides guidance for selecting the most suitable method for specific engineering problems.

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