# i am not getting the exact data for finite element model updating

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Susanta Barik on 29 Mar 2022
Commented: Susanta Barik on 29 Mar 2022
clear;
close all;
clc;
% __________ M3=40tons
% | | K3=50*10^6
% ---------- M2=45tons
% | | K2=50*10^6
% ---------- M1=50tons
% | | K1=50*10^6
% --- ---
set-up for stiffness matrix and other
m1=50000;
m2=50000;
m3=50000;
mass=diag([m1 m2 m3]);
fprintf('The mass matrix \n');
disp(mass)
k1=50*10^6;
k2=50*10^6;
k3=50*10^6;
stiffness=[k1+k2 -k2 0;-k2 k2+k3 -k3;0 -k3 k3];
fprintf('The stiffness matrix \n');
disp(stiffness)
Natural frequency(eigen value) and Mode shape(eigen vector) calculation
[v,d]=eig(stiffness,mass);
fprintf('lambda value \n');
disp(d);
w=[sqrt(d)];
w1=w(1,1);
w2=w(2,2);
w3=w(3,3);
W=[w1,w2,w3];
fprintf('The natural frequencies of this structure are as follows(HZ) \n');
disp(W)
fprintf('The mode shape of the structure \n');
disp(v)
fprintf('lambda value \n');
disp(d);
w=[sqrt(d)];
w1=w(1,1);
w2=w(2,2);
w3=w(3,3);
W=[w1,w2,w3];
fprintf('The natural frequencies of this structure are as follows(HZ) \n');
disp(W)
fprintf('The mode shape of the structure \n');
disp(v)
Individusal mode shapes vector
fprintf('individusal mode shapes \n');
v1=v(:,1)
v2=v(:,2)
v3=v(:,3)
Plotting of mode shape
% height=[0;3;6;9];
% for i=1:5
% subplot(1,3,i)
% plot([0; v(:,i)],height);
% xlabel('mode shape','FontSize',12);
% ylabel('Height of the structure','FontSize',12);
% title(['mode shape', num2str(i)],'FontSize',18);
% end
Sensitivity matrix
l1 = [1 0 0;0 0 0;0 0 0]; % DIFFERENTIATION OF STIFFNESS WRT K1
l2 = [1 -1 0;-1 1 0;0 0 0]; % DIFFERENTIATION OF STIFFNESS WRT K2
l3 = [0 0 0;0 1 -1;0 -1 1]; % DIFFERENTIATION OF STIFFNESS WRT K3
Mode shape decomposition
a111=0;
a112=(v2'*l1*v1)/(w1-w2);
a113=(v3'*l1*v1)/(w1-w3);
a121=0;
a122=(v2'*l2*v1)/(w1-w2);
a123=(v3'*l2*v1)/(w1-w3);
a131=0;
a132=(v2'*l3*v1)/(w1-w2);
a133=(v3'*l3*v1)/(w1-w3);
a211=(v1'*l1*v2)/(w2-w1);
a212=0;
a213=(v3'*l1*v2)/(w2-w3);
a221=(v1'*l2*v2)/(w2-w1);
a222=0;
a223=(v3'*l2*v2)/(w2-w3);
a231=(v1'*l3*v2)/(w2-w1);
a232=0;
a233=(v3'*l3*v2)/(w2-w3);
a311=(v1'*l1*v3)/(w3-w1);
a312=(v2'*l1*v3)/(w3-w2);
a313=0;
a321=(v1'*l2*v3)/(w3-w1);
a322=(v2'*l2*v3)/(w3-w2);
a323=0;
a331=(v1'*l3*v3)/(w3-w1);
a332=(v2'*l3*v3)/(w3-w2);
a333=0;
SENSITIVITY MATRIX FORMATION (CONSIDERING BOTH EIGEN VALUE AND MODE-SHAPE DECOMPOSITION)
s11 = v1'*l1*v1;
s12 = v1'*l2*v1;
s13 = v1'*l3*v1;
s21=a111*v1+a112*v2+a113*v3;
s22=a121*v1+a122*v2+a123*v3;
s23=a131*v1+a132*v2+a133*v3;
s31 = v2'*l1*v2;
s32 = v2'*l2*v2;
s33 = v2'*l3*v2;
s41=a211*v1+a212*v2+a213*v3;
s42=a221*v1+a222*v2+a223*v3;
s43=a231*v1+a232*v2+a233*v3;
s51 = v3'*l1*v3;
s52 = v3'*l2*v3;
s53 = v3'*l3*v3;
s61=a311*v1+a312*v2+a313*v3;
s62=a321*v1+a322*v2+a323*v3;
s63=a331*v1+a332*v2+a333*v3;
S = [s11 s12 s13;s21 s22 s23;s31 s32 s33;s41 s42 s43;s51 s52 s53;s61 s62 s63]
SENSITIVITY MATRIX FORMATION 2 (CONSIDERING ONLY EIGEN VALUE DECOMPOSITION)
% s11 = v1'*l1*v1;
% s12 = v1'*l2*v1;
% s13 = v1'*l3*v1;
% s21 = v2'*l1*v2;
% s22 = v2'*l2*v2;
% s23 = v2'*l3*v2;
% s31 = v3'*l1*v3;
% s32 = v3'*l2*v3;
% s33 = v3'*l3*v3;
% S=[s11 s12 s13;s21 s22 s23;s31 s32 s33];
UPDATING PARAMETER (CONSIDERING BOTH EIGEN VALUE AND MODE-SHAPE DECOMPOSITION)
K = [k1 k2 k3];
WA = [w1 v1' w2 v2' w3 v3'];
WM = [14.7257 -0.0015 -0.0027 -0.0038 35.4870 0.0029 0.0021 -0.0031 55.2413 -0.0031 0.0033 -0.0011];
K1 = K'+inv(S'*S)*S'*(WM'-WA')
UPDATING PARAMETER 2 (CONSIDERING ONLY EIGEN VALUE DECOMPOSITION)
% K = [k1 k2 k3];
% WA = [w1 w2 w3];
% WM = [13.3221 36.7237 51.7097];
% K1 = K'+inv(S*S')*S'*(WM'-WA')
##### 2 CommentsShowHide 1 older comment
Susanta Barik on 29 Mar 2022
I AM USING SENSITIVITY METHOD TO UPDATE FINITE ELEMENT DATA BUT WHAT THE RESULT I AM GETTING THAT IS NOT EXACT DATA . ALSO WHEN I AM COMPAIRING MY EXPERIMENTAL DATA WITH UPDATED DATA I AM GETTING NOT EXACT DATA