請用此 Handle URI 來引用此文件: http://hdl.handle.net/11455/18531
標題: 受到一移動外力的彈性基礎上的非線性樑之確定及隨機振動分析
Deterministic and Random Vibration Analysis of a Non-linear Beam on an Elastic Foundation Subjected to a Moving Load
作者: 劉勇男
U.N.Liou
關鍵字: moving load
移動外力
elastic foundation
nonlinear beam
random vibration
彈性基礎
非線性樑
隨機振動
出版社: 應用數學研究所
摘要: 本論文討論座落在彈性基礎上之非線性樑受到一移動外力的確定及隨機振 動, 此模型可模擬火車軌道或飛機跑道等等。本文考慮沿著樑方向的位移 及慣性力之效應, 因此, 導出了沿著樑方向的位移及垂直樑方向的位移之 聯立方程式。另外, 樑的剖面之隨機性質考慮成其平均線對位置而言為一 變數, 再重疊一隨機的不定性, 而且, 移動外力以等速度或等加速度沿樑 移動。本論文用 Galerkin 方法及有限單元法來計算樑的確定及統計動態 反應, 而且, 用內隱直接積分法 (implicit direct integration method ) 來解這一非線性的系統微分方程。此樑的側向位移之動態統計 性質則利用 Monte Carlo 模擬法求得。此外, 本文也用概率紙畫圖法來 判斷樑的中點位移的統計分佈。
In this paper, the deterministic and random vibration analysis of a nonlinear beam on an elastic foundation subjected to a moving load, which may simulate railway track, runway, etc, has been performed. The effects of longitudinal deflection and inertia have been considered so that the coupled equations of longitudinal and transverse deflections can be derived based on Bernoulli-Euler hypothesis. The randomness of the beam profile has been considered in such a way that the mean line of the beam is variable with respect to position in the vertical plane and is superimposed by stochastic uncertainty, and the moving load travells along the beam with constant velocity or acceleration. The deterministic and statistical dynamic responses of the beam have been calculated by using the Galerkin's method in conjunction with the finite element method, and the derived nonlinear system differential equation has been solved by using the implicit direct integration method. In particular, the standard deviation of the transverse deflection of the nonlinear beam have been calculated and presented by using the Monte Carlo simulation technique. Besides, the distribution of the midpoint deflection of the beam has been investigated by using the probability paper plot.
URI: http://hdl.handle.net/11455/18531
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