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題 名 | Free Vibration Analysis of Non-uniform Beams=非均勻斷面樑之振動分析 |
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作 者 | 徐明宏; | 書刊名 | 澎技學報 |
卷 期 | 8 2004.12[民93.12] |
頁 次 | 頁179-199 |
分類號 | 440.12 |
關鍵詞 | 自然頻率; 非均勻斷面樑; 微分值積法; DQM; Vibration; Non-uniform beam; Modified chebyshev sample point; |
語 文 | 英文(English) |
中文摘要 | 使用微分值積法來計算非均勻樑之振動行為,利用微分值積法推導具非均勻斷面樑的運動方程式,為驗證微分值積法用於分析此類非均勻樑結構的適用性,就具均勻等向性材料之非均勻斷面樑進行參數分析。探討微分值積法之取樣點數量、模態數量及權值對振動行為的影響,從提出的多個實例顯示,應用微分值積法能得到非常好的準確性。以多個數值實例產闡釋微分值積法分析步驟及其分析所獲致之結果,並與其他方法數值解之分析結果進行比較,藉以凸顯微分值積法應用於非均勻樑之振動行為之優點,為分析微分值積法中不同選點對計算結果精度之影響,亦就修正過的函數分佈取樣點與沒修正過的函數分佈取樣點所得結果進行比對,由不同非均勻斷面樑之振動分析結果顯示出修正過的函數分佈取樣點比沒修正過函數分佈取樣點用於分析此類問題更具有準確性,研究的結果與文獻的數值解做比較均甚吻合。 |
英文摘要 | The eigenvalue problems of non-uniform beams are numerically formulated using the differential quadrature method (DQM). The DQM is an effectively numerical technique in solving partial differential equations. The DQM can transform the differential equations into a set of algebraic equations n terms of the function values at each of the grid points. A modified Chebyshev sample point equation is proposed to determine the grid points of non-uniform beams. Appropriate boundary conditions accompanied the DQM to transform the partial differential equation of a non-uniform beam into a discrete eigenvalue problem. Numerical results indicated that the accuracy of the calculated results was improved significantly by employing the modified Chebyshev sample point equation. The grid point number effect on the accuracy variation of calculated natural frequencies is presented in this work. |
本系統中英文摘要資訊取自各篇刊載內容。