中文摘要：

根据梁模型端部的四种不同支承条件，将梁模型区分为一般支承梁、弹性支承梁、约束简支梁和约束悬臂梁四种，分别由各自的边界条件和梁弯曲振动模态函数的一般表达式推导出了这四种不同支承条件下梁模型弯曲振动的模态函数及其频率方程，计算得到了四种支承条件下梁模型的前两阶振动模态，具体分析了支承刚度对其特征值的影响。根据该方法，可以得出任意约束刚度下梁弯曲振动的任一模态及其特征值，其结果可以直接用于工程设计与分析。对于各种支承条件下的弹洼约束刚度，根据梁的实际支承情况合理选取。

英文摘要：

The beam model was classified into four styles ：generally supported beam,elastically supported beam,simply supported restrained beam and restrained cantilever beam according to their different supporting conditions. Four different eigenfunction and frequeney equation of them were deduced based on respective boundary conditions and the general expression of eigenfunetion. The first and the second mode of these four beam models under different supporting conditions were calculated and the effect of elastic coefficient on eigenvalue was analyzed. The other mode of these four beams and its eigenvalue can be obtained through the method illnstrated,the results can be directly used for the engineering design and analysis. The elastic coefficients of different supporting conditions to be treated come from the engineering issue according to their supporting environments.