中文摘要：

在空间域上采用只与结点有关的无网格方法离散，在时间域上采用精细积分方法求解．无网格离散过程中，利用伽辽金积分等效弱形式代替微分形式的控制方程，并用修正变分原理满足位移边界条件，采用移动最小二乘法求解离散的形函数，把形函数代入等效积分弱形式得到离散的二阶方程；精细积分过程中非齐次项采用Romberg积分．同时给出了两种不同边界条件的谐响应求解的两个数值算例，得到了精确的数值结果．

英文摘要：

An exact numerical method was explored for Timoshenko-beam harmonic response. In the space domain, element free method relative only with the node was used and governing equations are the equivalent weak form instead of differential form. The amendment variation principle was used to meet displacement boundary conditions and a least squares method to get the shape function. The shape function was taken into the equivalent of the weak points to get the second-order discrete equation. In the time domain, precise integration was used and Romberg integration was adopted for the non-homogeneous term. Finally, two examples of numerical results were obtained for the harmonic response problem at two different boundary conditions.