砖烟囱的竖向自振特性的一个计算方法

本文假设了接近砖烟囱实际截面面积的函数,推出了一个变系数的自由振动微分方程。对方程进行变量替换的演变得到了方程的三角函数解。根据边界条件得到的频率方程为超越方程,对超越方程求解,给出了前三个频率的一组曲线解。由这组曲线解,只需知道顶面和底面面积之比和高度,就可查得从等截面柱体到各种比例的变截面截锥体的竖向自振频率。

A Calculating Method for Vertical Free-Vibrating Character of Brick Chimney

In this paper, a cross-section function of brick chimney has been assumed based on traditional hypothesis and a variable coefficient free-vibrating differential equation has been derived. By means of variable substitution, a triangular function solution of the equation has been developed. The frequency equations, which have obtained through the boundary conditon, are superior equations. A group of curve solutions for the fh'st three frequencies have giuen, from which as far as the ratio of areas at the top and the bottom and the height of the chimney, the vertical freefrequency of a variable cross-section chimney can be looked up. The comprison bettween this paper and reference(2; indicates that the conception of this paper is clear, the calculating method simple and the accuracy quite well.