安庆师范学院学报(自然科学版)
安慶師範學院學報(自然科學版)
안경사범학원학보(자연과학판)
JOURNAL OF ANQING TEACHERS COLLEGE(NATURAL SCIENCE)
2014年
1期
1-5
,共5页
杆%梁连续系统%刚体模态%振荡性质%补充证明
桿%樑連續繫統%剛體模態%振盪性質%補充證明
간%량련속계통%강체모태%진탕성질%보충증명
rod and beam%rigid mode%oscillation properties%supplementary proof
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。
針對存在剛體運動形態的桿和Euler樑,藉助共軛繫統的概唸和性質,本文證明瞭它們都具有如下定性性質:設ui(x)是存在剛體運動形態的桿或Euler樑的連續繫統的第i(i =1,2,…)階位移振型,則對任意的2≤p≤q和不全為零的實常數ci(i =p,p +1,…,q),函數u(x)=cpup(x)+cp+1up+1(x)+…+cquq(x),0<x <l在區間(0,l)內的節點不少于p -1箇,而其零點不多于q -1箇。
침대존재강체운동형태적간화Euler량,차조공액계통적개념화성질,본문증명료타문도구유여하정성성질:설ui(x)시존재강체운동형태적간혹Euler량적련속계통적제i(i =1,2,…)계위이진형,칙대임의적2≤p≤q화불전위령적실상수ci(i =p,p +1,…,q),함수u(x)=cpup(x)+cp+1up+1(x)+…+cquq(x),0<x <l재구간(0,l)내적절점불소우p -1개,이기영점불다우q -1개。
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] .