Free vibration analysis of multiple-stepped beams by the differential quadrature element method
Free vibration analysis of multiple-stepped beams by the differential quadrature element method
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DOI：
10.1016/j.amc.2012.12.037
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发表时间：
2013-02
期刊：
影响因子：
--
通讯作者：
Xinwei Wang;Yongliang Wang
中科院分区：
文献类型：
--
作者：
Xinwei Wang;Yongliang Wang
本文提出了一种求解中性轴对齐的阶梯梁固有频率的高精度微分求积单元法。为了提高计算效率和精度，提供了计算加权系数的显式公式。各种例子与现有的解决方案进行了分析。为了显示的精度和效率的DQEM，结果进行了比较，以及通过使用有限元法（FEM）与非常精细的网格的数值解的分析。可以看出，收敛速度的DQEM是非常高的，DQEM可以产生非常准确的结果与现有的数值方法相比，少得多的计算工作。用DQEM方法得到的结果可以与现有的小数点后五位的解析解完全相同。该方法简单、有效，可方便地分析任意截面阶跃变化的梁。
The differential quadrature element method (DQEM) is proposed for obtaining highly accurate natural frequencies of multiple-stepped beams with an aligned neutral axis. To increase the computational efficiency and accuracy, explicit formulas are provided for computing the weighting coefficients. Various examples with existing solutions are analyzed. To show the accuracy and efficiency of the DQEM, results are compared to analytical as well as numerical solutions by using finite element method (FEM) with very fine meshes. It is seen that the rate of convergence of the DQEM is very high and the DQEM can yield very accurate results with much less computational effort as compared to existing numerical methods. The results obtained by the DQEM can be exactly the same as the existing analytical solutions to five places of decimals with a small number of grid points. The proposed method is simple and efficient, and can be used to analyze beams with any step changes in cross-section conveniently.