变截面欧拉梁自由振动分析的重采样微分求积法

采用重采样微分求积法求解了变截面欧拉梁的自由振动问题。推导了变截面梁的控制方程离散格式，采用重采样矩阵方法对边界条件进行处理，给出了变截面梁自由振动算法。采用本文方法对不同类型截面形式和不同边界条件的变截面梁进行自由振动分析，并和其他解法进行比较。计算结果表明，本文方法可以适用于不同变截面类型和不同边界条件，计算精度与解析解吻合良好，具有良好的收敛性能。在同等精度条件下网格点数少于现有计算方法。重采样转换矩阵边界处理方法相比于传统边界处理方法具有更快的收敛性能。

Resampling differential quadrature method for free vibration analysis of Euler beams with variable cross section

In this paper, the free vibration of Euler beams with variable cross-sections is analyzed by virtue of the resampling differential quadrature method.The discrete scheme of the governing equations of beams of variable cross-sections is derived and the boundary conditions are imposed by the resampling matrix method, and the detailed algorithm for the free vibration problem is established.Several beams with different cross-sections under different boundary conditions are analyzed and compared with the results computed by other methods.Results indicate that the accuracy of the proposed method is high.Moreover, the proposed method has excellent convergence and outperforms other methods compared in this paper.By comparing with the traditional replacing row method, the resampling matrix method has better convergence performance.