梁横向振动固有频率的数值计算  

Numerical Computation of Natural Frequencies of Transverse Vibration Beams

作　　者：钱波[1] 高建勇[1] 陈艳霞[1] 

机构地区：[1]西昌学院工程技术系,四川西昌615013

出　　处：《石河子大学学报（自然科学版）》2008年第1期87-90,共4页Journal of Shihezi University(Natural Science)

摘　　要：梁横向振动固有频率的计算在实际工程中具有重要意义,本文通过振型函数导出了求解梁横向振动固有频率的微分方程,根据梁的不同边界条件,利用有限差分法对梁进行不同的划分,由微分方程计算出不同划分的各阶固有频率,然后采用最小二乘法拟合求出各阶固有频率的准精确值,最后以一个有解析解的算例验证了该方法的计算结果的相对误差非常小,满足实际工程的精度要求,并以一变截面梁为例指出了变截面梁固有频率的计算方法,该方法具有编程简单、计算精度高、通用性强的优点。Differential equation to solve natural frequencies of transverse vibration beam is obtained from vibratory function which is significant in practical engineering, different orders of natural frequencies of different divisions to beams can be calculated from differential equation by means of finite differential method（FD）, then quasi-precision values of different orders are fitted by method of minimum squares. Finally the method given in the paper is verified by an example that has analytical solution which shows that relative errors of the calculative results are extraordinarily small and precisions can satisfy the demands for practical engineering, at the same time the method to calculate natural frequencies of non-uniform beams is also pointed out which possess the characteristic of simple program, high precisions, powerful tmiversality.

关 键 词：梁 横向振动 固有频率 数值计算 

分 类 号：TU311.4[建筑科学—结构工程]