隨著科技的進步，對產品品質及生產效率的要求也跟著提高。對軸向移動結構而言，生產效率之提升有賴於移動速度之提升，但較高的移動速度會衍生更多且更嚴重的振動問題，因此探討移動速度與張力對軸向移動結構的振動及穩定性之影響是有必要的。
本文研究軸向移動黏彈性平板受邊緣非均布激振力的動態穩定性。文中假設材料特性遵守凱爾文-福格特模型，平板在兩對邊為簡支撐端，另外兩對邊為自由端，平板在簡支撐端受到邊緣非均布激振力。本研究先探討平板在平面內之振動，再探討平板在平面外振動及穩定性。平板在平面內振動時，先利用漢米爾頓原理推導出平面內的運動方程式，並使用延伸的里茲法將方程式離散化，接著計算移動平板在平面內的自然頻率與模態，最後再求得平板受非均布激振力的響應與應力分布。平板在平面外振動時，先將求得的應力代入側向振動的運動方程式，並利用葛樂金法得到離散化的運動方程式，再求得側向振動的自然頻率與模態，接著利用模態分析法將運動方程式部分解耦，最後使用多尺度擾動法求得平板在週期激振力下的穩定邊界，並利用紐馬克數值積分法從暫態響應中，得到平板的穩定邊界。之後利用分析所得結果進行數值計算，並探討各參數對系統的自然頻率、響應及穩定性之影響。
數值結果顯示，在平面內振動隨著長寬比降低其臨界速度會增加，而顫動型不穩定會在臨界速度前發生。而在側向振動中，移動平板受到橫向對稱型式的激振力時，受力區域越集中，不穩定區域往低頻移動。

Dynamic Stability of Axially Moving Viscoelastic Plates Under Nonuniform Edge Excitations are investigated in this thesis. Assume that the material property of the plate obeys the Kelvin - Voigt model, and the excitations are arbitrarily distributed on two opposite simply-supported edges. This paper investigates the in-plane vibration of the plate first, and then investigates the out-of-plane vibration and the dynamic stability of the plate. For the in-plane vibration of the plate, the equations of the in-plane motion are first derived by Hamilton’s principle. Next, the extended Ritz method is used to obtain discretized system equations. Then, the natural frequencies and the mode shapes of the in-plane vibration of the axially moving plate are calculated. Finally, the displacements and the stress distributions of the plate subjected to nonuniform excitations are obtained. For the out-of-plane vibration of the plate, apply the stress distributions obtained previously to the equation of the out-of-plane motion of the plate, and the equation is discretized by generalized Galerkin’s method. Next, the natural frequencies and the mode shapes of the out-of-plane vibration of the plate are calculated. Then, a modal analysis method is used to partially uncouple the discretized system equations. Finally, the method of multiple scales is employed to determine the stability boundaries of the plate, and Newmark’s method is used to obtain the stability boundaries of plate from the transient responses of the plate. Numerical results are presented for the natural frequencies, response and stability of the plate under different system parameters.
Numerical results show that, as the aspect ratio increases, the critical speed of in-plane vibration of the moving plate decreases, and flutter instability occurs before the first critical speed is reached. In the out-of-plane vibration, when the moving plate is subjected to excitation forces symmetrically distributed in the transverse direction, the unstable regions move toward the low frequency range as the area of application becomes narrower.

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