摘要
本文以等直轴横向无阻尼自由振动微分方程为基础,建立了阶梯轴横向振动无量纲固有频率方程,进而将高阶微玢方程化为一阶微分方程组,采用四阶龙格—库塔法在微型计算机上进行数值运算,可一次求得阶梯轴一阶、二阶以至更高阶的固有频率,解法快速、准确,其精度接近有限元法.
Based on the undamped natural frequency equation of equal diameter shaft,this paper sets up dimensionless natural frequency equation of transv- erse vibration for staircase shaft. In order to simplify the calculation,the high-order differential equation was converted into system of first order differential equations,which is solved by means of a program with fourth order Runge-Kutta method,the frequencies of staircase shaft are found accurately and rapidly. This paper provided an important method for design of high-speed stair- case shaft.
关键词
阶梯轴
振动
固有频率
微分方程组
staircase shaft
natural frequency
system of differential equations
Ruuge-Kutta method
computer
