外伸梁离散系统模态的若干定性性质

摘要

Base on the basic oscillating properties of the frequencies and the displacement modes in the discrete system of the beam with overhang, it is proved that the stiffness matrices of conjugated system of a two-span beam with one cantilever is to be sign-oscillated. Then, the sign interchanges number of the flexural moment modes of a beam with one cantilever are determined. Furthermore, some qualitative propertiesof its displacement modes, rotation modes, moment modes and shearing force mode are given. The basic oscillating properties about two-span and three-span continuous beams having middle pinned are obtained practically in this paper as well.%在已证明外伸梁的差分离散模型频率和位移振型基本振荡性质的基础上，首先揭示了两跨外伸梁的共轭系统是一端铰支一端固定并有一个中间铰的两跨连续梁，证明了两跨外伸梁的共轭梁的刚度矩阵是符号振荡矩阵，进而确定了外伸梁的弯矩振型的符号改变数；由此进一步讨论了它的转角振型和剪力振型的符号改变数规律以及位移振型的其他一些定性性质．