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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/30871

Title: 權重動量法應用於動力方程式之分析
Applications of Weighted Momentum Principle to Dynamic Response Analysis of Equations of Motion
Authors: Ian Chen
Contributors: NTOU:Department of Harbor and River Engineering
Keywords: 權重動量法;動量平衡;衝擊載重;迭代法;權重法
weighted momentum principle;momentum equilibrium;impulsive loading;incremental-iterative solution;weight function
Date: 2012
Issue Date: 2012-04-13T07:45:49Z
Abstract: 對於衝擊載重的動力方程式,通常需要很小的時間步態進行計算,將會大幅增加計算量。本文所建立的權重動量法將以形狀函數模擬位移,將動力方程式乘上兩個權重函數並對時間積分,產生兩組動量平衡式,聯立求出速度和位移。權重動量法在處理自由振動的動力方程式,有不會發散也無數值阻尼等優點,對於連續載重或衝擊載重的動力方程式精確度均能達到四階。本研究將以三角形衝擊載重、三角形連續載重和矩形衝擊載重等問題探討權重動量法的精確度,並舉實例分析與Newmark法所得解作比較。在n維自由度的結構動力分析需要使用2n×2n的反矩陣運算,本研究提出權重動量的線性迭代法,僅需進行 n×n的反矩陣運算,經實例分析驗證只需迭代二至三次即可收斂,因此可藉由本文提出的迭代法,降低電腦運算時間。
It’s needed small time step to compute shock response for a structure under impulsive loadings but thus the cost of computing is increased. This study will show weighted momentum principle that use shape function to create the displacement of vibrating system then multiplying weight functions and integrating over the time step. For free vibration situation of an undamped SDOF system the method is stable ,no numerical damping and least fourth-order accuracy. For triangular continuous and impulsive loadings and rectangle impulsive loadings the method is also least fourth-order accuracy. We will compare it with Newmark method. For an n-DOFs system, the dimension of matrix equation in state space will be expanded to 2n by 2n as well. The incremental-iterative solution procedure for linear structural dynamics is established to simplify computing matrixs to n by n and the convergence is fast.
URI: http://ethesys.lib.ntou.edu.tw/cdrfb3/record/#G0M97520017
Appears in Collections:[河海工程學系] 博碩士論文

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