悬臂梁系统复模态计算时用eig求得的特征值存在非共轭现象
相关程序如下:
length1=0.8;er=2.8e3;ee=68.9e9;wid=0.06;high=0.016;mm=length1*er*wid*high;
ei=wid*high*high*high/12;ea=wid*high;
ne=5;nfe=4;nf=10;el=length1/ne;%输入单元数、单元自由度数、系统总自由度数、计算单元长度
ndg=[11,12,1,6;1,6,2,7;2,7,3,8;3,8,4,9;4,9,5,10];%输入各单元自由度编号
em=[156,-22*el,54,13*el;-22*el,4*el*el,-13*el,-3*el*el;54,-13*el,156,22*el;13*el,-3*el*el,22*el,4*el*el];
em=em*er*ea*el/420;%计算单元质量阵
ek=[12,-6*el,-12,-6*el;-6*el,4*el*el,6*el,2*el*el;-12,6*el,12,6*el;-6*el,2*el*el,6*el,4*el*el];
ek=ek*ee*ei/el/el/el;%计算单元刚度阵
sk=zeros(nf,nf);sm=zeros(nf,nf);%形成空的总刚度和质量矩阵
m=zeros(4);
for kk=1:ne,
for i=1:nfe,
m(i)=ndg(kk,i);
end
for i=1:nfe,
mi=m(i);
if(mi<=nf),
for j=1:nfe,
mj=m(j);
if(mj<=nf),
sk(mi,mj)=sk(mi,mj)+ek(i,j);
sm(mi,mj)=sm(mi,mj)+em(i,j);
end
end
end
end
end
[V,D]=eig(sk,sm);%求解广义特征值问题
fre=sqrt(diag(D))/2/pi;%计算无阻尼各阶固有频率
sc2=0.006*eye(nf,nf)+0.9*sm+(8e-5)*sk;
% % A1=[sc2,sm;sm,zeros(nf,nf)];B1=[sk,zeros(nf,nf);zeros(nf,nf),-sm];
% A1=[zeros(nf,nf),sm;sm,sc2];B1=[-sm,zeros(nf,nf);zeros(nf,nf),sk];
% [VV,DD]=eig(-B1,A1);
% lemda=diag(DD);
用eig求得的系统特征值
lemda =
1.0e+05 *
-2.1627 + 0.0000i
-0.9152 + 0.0000i
-0.3209 + 0.0000i
-0.1249 + 0.1248i
-0.1249 - 0.1248i
-0.2044 + 0.0000i
-0.0584 + 0.1057i
-0.0584 - 0.1057i
-0.1446 + 0.0000i
-0.1324 + 0.0000i
-0.0212 + 0.0695i
-0.0212 - 0.0695i
-0.0077 + 0.0431i
-0.0077 - 0.0431i
-0.0020 + 0.0221i
-0.0020 - 0.0221i
-0.0003 + 0.0079i
-0.0003 - 0.0079i
-0.0000 + 0.0013i
-0.0000 - 0.0013i
请问这是什么情况?一般情况下eig求得的特征值不是应该两两共轭的吗?这里面为什么会有6个互不相等的实数存在呢?
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