摘要
将悬臂梁的自由振动挠度函数假设为各阶振型函数与关于时间的广义坐标乘积的线性组合,推导得到了系统动能与弯曲变形能的级数形式的表达式。运用Lagrange运动方程得到了悬臂梁的前4阶固有频率方程及其解。并将计算结果与解析解进行了对比,分析了高阶固有频率误差值逐步增加的原因,提出了改进方法。研究表明,只要能够选取合适的振型函数,该方法对于不同边界条件的梁(柱)结构具有广泛的适应性,有着明显的理论意义和工程意义。
Under the assumming of the free vibration defection function of a cantilever beam being the linear combination of multiple vibration mode functions with universal coordinate product about the time,the series expression of the beam＇s kinetic energy and bending deformation energy is deduced and obtained.Using Lagrange motion equation,the frout four-order natural frequency equation of the beam is established and its solution is obeained.Furthermore,a comparison is made between above mentioned results and its analytic solution and then,the reasons coused the natural frequency error increasing is analyzed and improred inethod is put forword too.This method has a wide application to the beam structures with various boundary conditions if an appropriate vibration mode function is adoped and this research work has a great significance in theory as well as in engineering.
出处
《青海大学学报（自然科学版）》
2011年第1期12-15,共4页
Journal of Qinghai University(Natural Science)
作者简介
黄永玉（1976一），男，青海大通人，副教授，兰州理工大学在读硕士研究生。研究方向：机械震动。
