本研究係考慮雙線性遲滯系統於雙頻外力作用下，探討其因外力頻率比n的改變所產生的振幅反應特性。分析結果顯示系統反應隨著n由1開始遞增，可出現截然不同之反應特徵；在n小於1.1時，系統出現顯著之拍頻現象，而當n接近偶數時，則以顯性之振態疊加呈獻。為進一步釐清此一反應差異所引發之工程意涵，本文定義一反應振幅係數 以觀察系統在穩態反應下之振幅強弱，研究亦推導線性狀態下之 解析解，用以比較非線性計算出之 值。比較結果發現 值具顯著之雙峰現象，直接呼應外力之雙頻特色，遲滯迴圈之非線性特質產生不同程度之勁度軟化效應，而導致雙峰偏移與 值大小之調整。

Dynamic responses of bi-linear hysteretic systems under two-frequency excitations characterized by a frequency ratio, n, are studied in this thesis. The analytical results show markedly different response characteristics as the excitation parameter n increases from unity. The classical beat phenomenon can be found for most cases with an n smaller than 1.1. On the other hand, a two-mode superposition in displacement is obvious when n is closer to an even number. To further explore its engineering implication, the indicated response features are compared based on a steady-state amplitude parameter referring to the Response Amplitude Factor, . An analytical expression of the parameter is first derived for the linear system and is then compared with numerical solutions evaluated for the nonlinear systems. The spectra demonstrate a two-peak response feature that conforms to the external excitation frequencies. The effects of stiffness softening are also clear as evidenced by a left-switch trend in the response peaks as the degree of nonlinearity increases. However, the variation in the peak magnitude is difficult to quantify

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