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中文摘要：
基于Hermite再生核无网格近似，建立了Euler梁自由振动分析的伽辽金无网格离散方程．针对常见的几种典型边界条件的Euler梁自由振动问题，详细分析了前两阶频率的误差和收敛性．结果表明，与传统仅采用挠度近似的伽辽金无网格法和Hermite有限元法相比，考虑节点转角对挠度近似影响的Hermite无网格方法具有更高的精度，为Euler梁振动分析提供了一种高精度的数值方法．
英文摘要：
A free vibration analysis of Euler beam using a Galerkin meshfree formulation with the Hermite reproducing kernel approximation is presented. Based upon the proposed approach the free vibration analysis of Euler beam with various typical boundary conditions is performed and the error and convergence behavior of the fundamental and second frequencies are studied in details. It is uniformly confirmed that compared with the conventional reproducing kernel meshfree method and the Hermite finite element method, the present method that incorporates the slope influence into the deflection approximation shows the most favorable solution accuracy and thus provides a very effective numerical tool for accurate vibration analysis of Euler beam.
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