How to find mode shape
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this is my code for one shaft 0 disk. but I don't know how to plot mode shape I can't find b.
nel1=14;
nnel=2; %
ndof=4; %
phase1=0; %
nb1=2; %
snode1=nel1+1; %
nnode1=(nel1+1); %
bpo1=[0,1.4]; %
edof=nnel*ndof; %
sdof=snode1*ndof; %
L1=1.4; %
Es1=2e11; %
v1=0.3; %
Ros1=7800; %
Gs1=Es1/(2*(1+v1)); %
G1=Gs1;
rr1=zeros(2,nel1); %
rr1(1,:)=0.05; %
rr1(2,:)=0; %
MM1=zeros(sdof,sdof); % initialization of M system matrix
CC1=zeros(sdof,sdof); % initialization of C system matrix
KK1=zeros(sdof,sdof); % initialization of K system matrix
GG1=zeros(sdof,sdof)
gcoord1=zeros(nnode1,1);
for i=1:nnode1;
gcoord1(i)=gcoord1(i)+(i-1)/nel1*L1;
end
for i=1:nel1;
for j=1:nnel;
nodes1(i,j)=i+j-1;
end
end
for iel=1:nel1;
nl1=nodes1(iel,1); nr1=nodes1(iel,2);
L21=gcoord1(nr1)-gcoord1(nl1);
L11=gcoord1(nl1);
rso1=rr1(1,iel);
rsi1=rr1(2,iel);
m1=rsi1/rso1;
kpran1=(6*(1+v1)*(1+m1^2)^2)/((7+6*v1)*(1+m1^2)^2+(20+12*v1)*m1^2);
o1=(12*Es1*(1/4*pi*(rso1^4-rsi1^4)))/(kpran1*Gs1*(pi*(rso1^2-rsi1^2))*L21^2);
As1=pi*(rso1^2-rsi1^2);
Isd1=1/4*pi*(rso1^4-rsi1^4);
Isp1=1/2*pi*(rso1^4-rsi1^4);
[m1,k1,g1]=residualMCK1(o1,L1,Ros1,L11,L21,As1,Isp1,Isd1,Es1,kpran1,Gs1);
mm1=m1;
kk1=k1;
gg1=g1;
for i=1:edof
start1 = (iel-1)*(nnel-1)*ndof;
ii=start1+i;
for j=1:edof
jj=start1+j;
MM1(ii,jj)=MM1(ii,jj)+double(mm1(i,j));
KK1(ii,jj)=KK1(ii,jj)+double(kk1(i,j));
GG1(ii,jj)=GG1(ii,jj)+double(gg1(i,j));
end
end
end
KKB1=zeros(sdof,sdof);
KKB2=zeros(sdof,sdof);
CCB1=zeros(sdof,sdof);
CCB2=zeros(sdof,sdof);
Cyy1=0;
Cyy2=0;
Cyz1=0;
Czy1=0;
Czz1=0;
Czz2=0;
Kyy1=1e12;
Kyy2=1e12;
Kyz1=0;
Kzy1=0;
Kzz1=1e12;
Kzz2=1e12;
Kb1=[Kyy1 Kyz1;Kzy1 Kzz1];
Cb1=[Cyy1 Cyz1;Czy1 Czz1];
Kb2=[Kyy2 Kyz1;Kzy1 Kzz2];
Cb2=[Cyy2 Cyz1;Czy1 Czz2];
for ib1=1:nb1;
start1=bpo1(ib1)/L1*nel1*ndof;
for i=1:2;
ii=start1+i;
for j=1:2;
jj=start1+j;
KKB1(ii,jj)=KKB1(ii,jj)+Kb1(i,j); % combine bearing to global
CCB1(ii,jj)=CCB1(ii,jj)+Cb1(i,j);
KKB2(ii,jj)=KKB2(ii,jj)+Kb2(i,j); % combine bearing to global
CCB2(ii,jj)=CCB2(ii,jj)+Cb2(i,j);
end
end
end
MMMM=MM1;
CCCC1=CC1+CCB1;
CCCC2=CC1+CCB2;
KKKK1=KK1+KKB1;
KKKK2=KK1+KKB2;
GGGG=GG1;
o=zeros(sdof,sdof);
n=0;
XXYY=zeros(1,1);
Oma1=0;
n=n+1;
XXYY(n)=Oma1;%*60/2/pi;
E=[o,-MMMM;MMMM,(CCCC1)+(Oma1*GGGG)];
F=[MMMM,o;o,KKKK1];
EF=-inv(E)*F;
w=sort(abs(imag(eig(EF))));
wwwa=abs(imag(eig(EF)));
[C,D]=eig(EF);
K=imag(C);
R=real(C);
ww1(:,n)=w;%*60/2/pi;
A0=imag(D);
for k=1:sdof*2
A1(k,1)=A0(k,k);
end
for i=1:2:sdof*2-1
QQQ(:,i)=C(:,i)*D(i,i)+C(:,i+1)*D(i+1,i+1);
end
QQQ(:,sdof*2)=C(:,sdof*2)*D(sdof*2,sdof*2);
QQQV1=QQQ(sdof+1:ndof:sdof*2,:);
QQQW1=QQQ(sdof+2:ndof:sdof*2,:);
QQQB1=QQQ(sdof+3:ndof:sdof*2,:);
QQQR1=QQQ(sdof+4:ndof:sdof*2,:);
QQQV2=QQQ(sdof*1.5+1:ndof:sdof*2,:);
QQQW2=QQQ(sdof*1.5+2:ndof:sdof*2,:);
QQQU2=QQQ(sdof*1.5+3:ndof:sdof*2,:);
QQQB2=QQQ(sdof*1.5+4:ndof:sdof*2,:);
QQQR2=QQQ(sdof*1.5+5:ndof:sdof*2,:);
QQQA2=QQQ(sdof*1.5+6:ndof:sdof*2,:);
% plot mode shape % figure(1) %coupled b=117; plot(1:snode1,QQQV1(:,b),1:snode1,QQQW1(:,b),'linewidth',0.5); title('Mode 1 = 633.65 (rad/s)') legend('Driving-V','Driving-W') ;
figure(5)
%coupled
b=31;
plot(1:snode1,QQQV1(:,b),1:snode1,QQQW1(:,b),'linewidth',0.5);
title('Mode 2 = 2550 (rad/s)')
legend('Driving-V','Driving-W') ;
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