軸向移動平板在工程上應用非常廣泛，加上現今對產品品質及生產效率要求隨科技發展而提升，故對軸向移動平板之研究在過去數十年受到關注。因平板的軸向移動速度及所承受之平面應力對其靜態及動態行為影響很大，故本文擬探討軸向移動黏彈性平板受隨機邊緣張力之隨機穩定性問題。本文假設黏彈性平板之材料特性遵守凱爾文-福格特模型，而平板在軸向兩對邊為簡支撐邊界，另兩對邊為自由邊界，且平板在簡支撐邊緣承受隨機邊緣張力。文中先以牛頓第二運動定律及古典板理論推導平板的側向運動方程式，再利用漢米爾頓原理與延伸的里茲法計算出靜止平板承受靜態邊緣張力的平面內位移，接著將位移代入應力與應變關係式，求得平板應力分佈，再以葛樂金法得到離散化的側向運動方程式，並利用模態分析法將運動方程式部分解耦合，最後以統計平均法求得平板的隨機穩定邊界，並以數值探討平板各參數對平板隨機穩定邊界之影響。
數值結果顯示，平板的隨機穩定性和隨機邊緣張力之形式關係不大，但邊緣張力之隨機部分的合力越小，則平板的穩定區域越大，且邊緣張力之靜態部分越小、速度越快和長寬比(a/b)越大，則平板的穩定區域越小。

Random stability of axially moving viscoelastic plates under stochastic edge tension is investigated in this thesis. It is assumed that the material property of the plate obeys the Kelvin-Voigt model, and the plate is simply-supported on two opposite edges, and is free on the other two edges. The plate is subjected to stochastic edge tension on the simply-supported edges. First, the governing partial differential equation of out-of-plane motion of the plate is derived by Newton’s second law under classical Kirchhoff thin plate assumptions. Then, Hamilton’s principle and the extended Ritz method are used to obtain the in-plane stress distribution of the plate. Next, the equation of the out-of-plane motion of the plate is discretized by generalized Galerkin’s method, and the discretized equations of the motion of the plate is partially uncoupled by modal analysis. Finally, the Ito equation for the system response amplitude is obtained by the stochastic averaging method, and the mean-square stability criterion is determined. Numerical results are presented for mean-square stability boundaries of the plate under different system parameters.
Numerical results show that a decrease in stochastic part of the edge tension will enlarge the stable region of the plate. A smaller static part of the edge tension, a higher axial speed, and a larger aspect ratio result in a smaller stable region of the plate.

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