Finding Natural frequencies and Mode shapes of an undamped 2 DOF Systems through Matlab

Hello, I'm a student and I look for a solution for Matlab. I'm quite beginner to use Matlab. Could you pls help me to write it through Matlab? I need how to write these codes through Matlab.

Thank you for all your supports and helps!

Answer 1

[AVB]

Try using below .... change m1, m2 , k1 and k2 with your problem values.

clc;

m1 = 5;
m2 = 10;
k1= 1500;
k2 = 6500;

m = [m1 0; 0 m2];
k = [(k1 + k2) -k2; -k2 k2];

eigsort(k,m);

function [u,wn]=eigsort(k,m)
Omega=sqrt(eig(k,m));
[vtem,~]=eig(k,m);
[wn,isort]=sort(Omega);
il=length(wn);
for i=1:il
v(:,i)=vtem(:,isort(i));
end
disp("The natural frequencies are (rad/sec)")
wn
disp("\nThe eigenvectors of the system are")
v
disp("Ratios of eigenvectors are:\n")
A1_A2_1 = v(1,1)/v(2,1)
A1_A2_2 = v(1,2)/v(2,2)
figure(1)
plot([0,1,2,3], [0,A1_A2_1,1,0],'b-s', 'LineWidth',2, 'MarkerSize',10);
hold on;
plot([0,1,2,3], [0,-A1_A2_2,-1,0],'r-s', 'LineWidth',2, 'MarkerSize',10);
hold off; ylabel('Eigne Vector Ratio'); xlabel('Mass Number'); xticks([1 2]);
legend('Mode 1', 'Mode 2')
end

[Irshad Ahamed]

If I were to use 4 DOF, how would I need to modify this code?

Answer 2

[Bertan Parilti]

Thank you a lot!

Answer 3

[Rakesha]

clc;

m1 = 5;

m2 = 10;

k1= 1500;

k2 = 6500;

m = [m1 0; 0 m2];

k = [(k1 + k2) -k2; -k2 k2];

eigsort(k,m);

function [u,wn]=eigsort(k,m)

Omega=sqrt(eig(k,m));

[vtem,~]=eig(k,m);

[wn,isort]=sort(Omega);

il=length(wn);

for i=1:il

v(:,i)=vtem(:,isort(i));

end

disp("The natural frequencies are (rad/sec)")

wn

disp("\nThe eigenvectors of the system are")

v

disp("Ratios of eigenvectors are:\n")

A1_A2_1 = v(1,1)/v(2,1)

A1_A2_2 = v(1,2)/v(2,2)

figure(1)

plot([0,1,2,3], [0,A1_A2_1,1,0],'b-s', 'LineWidth',2, 'MarkerSize',10);

hold on;

plot([0,1,2,3], [0,-A1_A2_2,-1,0],'r-s', 'LineWidth',2, 'MarkerSize',10);

hold off; ylabel('Eigne Vector Ratio'); xlabel('Mass Number'); xticks([1 2]);

legend('Mode 1', 'Mode 2')

end