弹性支承弯曲振动梁的频率方程及其特征值分析

由等截面直梁弯曲振动微分方程及其通解和弹性支承、中间固定支承与自由端的边界条件，推导出弹性支承弯曲振动梁的频率方程的解析表达式．并利用数值方法（二分法）计算出在不同弹簧弹性系数和梁的弯曲刚度下弯曲振动梁的前两阶特征值，分析了梁的弯曲刚度对特征值的影响．另外，通过给出的在不同中间固定支承位置下特征值随弹簧弹性系数变化的曲线，分析了弹簧弹性系数对特征值的影响．

Frequency Equation of Elastic Supported Beams and Analysis of Their Eigenvalues

Based on the bending vibration differential equation and its general solution of the beams, the analytical expressions of frequency equation of bending vibration beams with the elastic support have been derived under the boundary conditions including the elastic support, the intermediate fixed support and free end. And the first two-order eigenvalues of the beams have been calculated by using numerical methods （dichotomy） when the coefficient of the torsion springs and the bending rigidity of the beams are different and the influences on the eigenvalues by the bending stiffness of the beams have been analyzed. In addition, through the given variation curve that the eigenvalues are changing along with the coefficient of the torsion springs at each location of the intermediate fixed support, the influences on the eigenvalues by the coefficient of the torsion springs have been analyzed.