多跨梁离散系统的频谱和模态的定性性质  

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

作　　者：王其申[1] 吴磊[1] 王大钧[2] 

机构地区：[1]安庆师范学院物理与电气工程学院,安庆246011 [2]北京大学湍流与复杂系统国家重点实验室北京大学工学院力学与空天技术系,北京100871

出　　处：《力学学报》2009年第6期947-952,共6页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(10772001)~~

摘　　要：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。The qualitative properties of the frequency spectrum and modes were studied extensively for the nonhomogeneous single span beams, in which the discrete and continuous systems were included. However, the qualitative properties about the multispan beams were studied and only shown in the book “Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems” published by Gantmakher, F. P. and Krein, M. G. The discrete model given in this book was formed by adding several masses to massless continuous system of the multispan beam, and the adopted method was based on the influence function of the beam, related to the positive systems. Nevertheless, the conditions about the positive systems were not discussed in the above-mentioned book. In this paper the difference discrete models of the multispan beam with arbitrary supports at two ends are established. According-the：the above book, the flexibility coefficient of the above models corresponding to the positive single span beam systems is given. The oscillating property of the flexibility matrix of the multispan beam is determined based on that of the positive single span beam systems by introducing beams are obtained.

关 键 词：多跨梁 柔度矩阵 频谱 模态 定性性质 

分 类 号：O327[理学—一般力学与力学基础] O241.3[理学—力学]