非均匀变截面梁的稳定和自由振动的阶梯折算法

The Step-Reduction Method for Buckling and Free Vibration of Nonuniform Beams with Variable Cross Section

本文利用阶梯析算法给出非均匀变截面梁的稳定和自由振动问题的一般解.问题最后归结为求解一个超越代数方程.这个代数方程用解析的形式给出,因此对优化特别方便.在文中给出收敛性证明.文末给出算例,表明利用本文的方法,可得到满意的结果.

In this paper,a general solution for buckling and free vibration ofnonuniform beams with variable cross section is obtained by the step-reductionmethod.Finally,it is only necessary to solve a nonlinear algebraic equa.tion,which is expressed as an analytic form,and the convergence of which caneasily be proved.Two numerical examples are given at the end of the paperto indicate the satisfactory results obtained by the step-reduction method.