| 存在刚体模态的杆、梁连续系统某些振荡性质的补充证明 |
| |
| 引用本文： | 王其申,王大钧.存在刚体模态的杆、梁连续系统某些振荡性质的补充证明[J].安庆师范学院学报(自然科学版),2014(1):1-5. |
| |
| 作者姓名： | 王其申 王大钧 |
| |
| 作者单位： | 安庆师范学院物理与电气工程学院;北京大学 |
| |
| 基金项目： | 国家自然科学基金(10772001)资助 |
| |
| 摘 要： | 针对存在刚体运动形态的杆和Euler梁，借助共轭系统的概念和性质，本文证明了它们都具有如下定性性质：设ui（x）是存在刚体运动形态的杆或Euler梁的连续系统的第i（i ＝1，2，…）阶位移振型，则对任意的2≤p≤q和不全为零的实常数ci（i ＝p，p ＋1，…，q），函数u（x）＝cpup（x）＋cp＋1up＋1（x）＋…＋cquq（x），0＜x ＜l在区间（0，l）内的节点不少于p -1个，而其零点不多于q -1个。
|
| 关 键 词： | 杆 梁连续系统 刚体模态 振荡性质 补充证明 |
The Supplementary Proof of Some Oscillation Property for Continuous Systems of Rod and Beam Having Rigid Modes |
| |
| WANG Qi-shen,WANG Da-jun.The Supplementary Proof of Some Oscillation Property for Continuous Systems of Rod and Beam Having Rigid Modes[J].Journal of Anqing Teachers College(Natural Science Edition),2014(1):1-5. |
| |
| Authors: | WANG Qi-shen WANG Da-jun |
| |
| Institution: | 1. Department of Physics, Anqing Teachers College, Anqing 246133, China; 2. State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China) |
| |
| Abstract: | Using the idea and properties of the conjugated systems, we prove the following oscillation properties for the contin-uous systems of rod and beam having rigid modes in the present paper： Let ui（x） =（i =1,2,…） are the i-th displacement modes of continuous systems of rod or beams having rigid mode.Then,for any set of real numbers ci（i =p,p ＋1,…,q;2≤p≤q） that does not vanish simultaneously, the function u（x） =cpup（x） ＋cp＋1up＋1（x） ＋… ＋cquq（x） has at least p-1 nodes and no more than q -1 zeroes in the interval 0,l] . |
| |
| Keywords: | rod and beam rigid mode oscillation properties supplementary proof |
| 本文献已被 CNKI 维普 等数据库收录！ |
|
