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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
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
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

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.
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