摘要
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.
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.
出处
《青岛理工大学学报》
CAS
2009年第6期99-102,共4页
Journal of Qingdao University of Technology
关键词
弹性支承
弯曲振动梁
频率方程
特征值
elastic support
bending vibration beam
frequency equation
eigenvalue
作者简介
任正义（1962-），男，黑龙江哈尔滨人．博士，教授，主要从事机械设计及理论研究．E-mail：yetangyt@eyou．com．
