存在刚体模态的杆、梁离散系统某些振荡性质的补充证明  

Supplementary Proof of Some Oscillation Property for Discrete Systems of Rod and Beam Having Rigid Modes

作　　者：王其申[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,安徽安庆246011 [2]北京大学工学院力学与空天技术系,北京100871

出　　处：《力学季刊》2014年第2期262-269,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(10772001)

摘　　要：工程实际中大量存在具有刚体运动形态的杆和Euler梁.针对存在刚体运动形态的杆和Euler梁的具有n个自由度的离散系统,借助共轭系统的概念,从共轭系统所具有的振荡性质出发,证明了它们都具有如下定性性质:对任意的2≤p≤q≤n,由系统的第p阶至第q阶位移振型线性组合而成的矢量u=cpu(p)+cp+1u(p+1)+…+cqu(q),其分量序列的最小变号数不少于p-1,而其分量序列的最大变号数不多于q-1.这一结果对于相关理论的完整性是必须的,同时有着重要的工程意义和应用价值.There are a great deal of rods and beams with rigid modes in engineerings. To use idea and properties of the conjugated system and its oscillation properties, the following oscillation properties for the discrete systems of rod and beams, which have rigid mode and n degrees of freedoom, were proved in this paper： The minimum number of sign reversals is not less than p - 1 and the maximum number of sign reversals is not more than q - 1 in the vector u=cpu（p）＋cp＋1u（p＋1）＋…＋cqu（q）, , which is composite vector from P-th order to q-th order （2 ≤ p ≤ q ≤ n ） displacement modes of the corresponding systems. These properties are necessary for theoretical complete and have important engineering meaning and application value.

关 键 词：杆、梁离散系统 刚体模态 振荡性质 补充证明 

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