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] .%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。
展开▼
