自由間隙為全動式控制面常見之結構非線性來源，並可能顯著影響其跨音速氣動彈性行為。本研究以葉片彈簧拘束剛性機翼形成單一俯仰自由度的代表性全動翼模型，透過風洞實驗與數值模擬探討初始攻角與自由間隙對平衡位置、翼面扭轉響應、極限循環振盪（LCO）、震波動態及近壁面流場結構的影響。
研究結果顯示，自由間隙不僅會改變機翼平衡位置，亦會促進LCO發生。流固耦合模擬成功捕捉實驗觀察到之主要氣動彈性趨勢，且平衡位置預測誤差約為0.5°。流場觀測結果顯示，穩態響應案例以正常震波為主，而LCO案例則出現伴隨強烈震波／邊界層交互作用的λ型震波。頻譜分析發現系統存在約220 Hz與340 Hz兩種主要響應機制。進一步透過POD分析、互相關分析發現頻率鎖定現象發生在LCO案例，顯示220 Hz響應對應於預應力結構模態，而340 Hz響應則與自由間隙及環境振動有關。研究結果證實自由間隙對全動翼之平衡位置偏移、LCO起始以及流固耦合特性具有關鍵影響。

Free-play is a common source of structural nonlinearity in all-movable control surfaces and can significantly affect transonic aeroelastic behavior. This study investigates the transonic fluid–structure interaction characteristics of a representative all-movable wing, which consisting of a rigid wing restrained by a leaf spring in only pitch-DOF, through both experimental and numerical approaches. Parametric studies of the initial angle of attack and free-play level are conducted to examine their effects on equilibrium position, wing twist response, limit-cycle oscillation (LCO), shock dynamics, and near-wall flow structures.
The results show that increasing free-play not only shifts the wing equilibrium position but also promotes the onset of LCO. The FSI simulations capture the major aeroelastic trends observed in the experiments and predict the equilibrium position within approximately 0.5° of the measured value. Flow-field observations reveal standing-shock structures in steady-response cases and λ-shock structures associated with shock-wave/boundary-layer interaction in LCO cases. Spectral analysis identifies that two dominant mechanisms coexist with frequencies near 220 Hz and 340 Hz. Further POD and cross-correlation analyses indicate that the frequency lock-in occurs for the LCO cases, providing strong evidence 220 Hz response corresponds to the prestressed structural mode, while the 340 Hz response is associated with free-play and environmental vibration effects. The results demonstrate that free-play plays a critical role in the equilibrium shift, LCO onset, and fluid–structure coupling characteristics of transonic all-movable wings.

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