多跨梁离散系统的频谱和模态的定性性质

采用差分法建立了两端任意支承多跨梁的差分离散模型，对只具有两端支承的单跨梁是正系统的情形，导出了对应的多跨梁差分离散系统的柔度系数；从单跨梁正系统的刚度矩阵的符号振荡性出发，通过引入辅助系统，讨论了多跨梁的柔度矩阵的振荡性，确定了对应于单跨梁正系统的多跨梁差分离散系统的频谱和模态的一系列定性性质. 

SOME QUALITATIVE PROPERTIES OF FREQUENCY SPECTRUM AND MODES OF DIFFERENCE DISCRETE SYSTEM OF MULTIBEARING BEAM

The qualitative properties of the frequency spectrum andmodes were studied extensively for the nonhomogeneous single spanbeams, in which the discrete and continuous systems were included. However,the qualitative properties about the multispan beams were studied and onlyshown in the book ``Oscillation Matrices and Kernels and Small Vibrations ofMechanical Systems' published by Gantmakher, F. P. and Krein, M. G. Thediscrete model given in this book was formed by adding several masses tomassless continuous system of the multispan beam, and the adopted method wasbased on the influence function of the beam, related to the positivesystems. Nevertheless, the conditions about the positive systems were notdiscussed in the above-mentioned book. In this paper the difference discretemodels of the multispan beam with arbitrary supports at two ends areestablished. According to the above book, the flexibility coefficient of theabove models corresponding to the positive single span beam systems isgiven. The oscillating property of the flexibility matrix of the multispanbeam is determined based on that of the positive single span beam systems byintroducing an auxiliary system. A series of qualitative properties of thefrequency spectrum and modes of the multispan beams are obtained.