eigen value what i am getting from matlab software that is not exact when i am compairing with hand calculated value and the mode shape i am getting is reverse

format long g
m1=50000;
m2=50000;
m3=50000;
mass=diag([m1 m2 m3]);
fprintf('The mass matrix \n');

The mass matrix 

disp(mass)

       50000           0           0
           0       50000           0
           0           0       50000

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');

The stiffness matrix 

disp(stiffness)

   100000000   -50000000           0
   -50000000   100000000   -50000000
           0   -50000000    50000000

%Natural frequency(eigen value) and Mode shape(eigen vector) calculation FOR ANALYTICAL VALUE
[v,d]=eig(stiffness,mass);
fprintf('lambda value \n');

lambda value 

disp(d);  

          198.062264195162                         0                         0
                         0          1554.95813208737                         0
                         0                         0          3246.97960371747

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');

The natural frequencies of this structure are as follows(HZ) 

disp(w)

          14.0734595673971          39.4329574352137          56.9822744695003

fprintf('The mode shape of the structure \n');

The mode shape of the structure 

disp(v)

      -0.00146679475269089       0.00329585789213623      -0.00264307281555424
      -0.00264307281555424       0.00146679475269089       0.00329585789213623
      -0.00329585789213623      -0.00264307281555424      -0.00146679475269089

%Normalization of mode shape vectors
% for i=1:3
%     v(:,i)=v(:,i)/v(3,i);
% end

% Individusal mode shapes vector

fprintf('individusal mode shapes \n');

individusal mode shapes 

v1=v(:,3)

v1 = 3×1

-0.00264307281555424 0.00329585789213623 -0.00146679475269089

v2=v(:,2)

v2 = 3×1

0.00329585789213623 0.00146679475269089 -0.00264307281555424

v3=v(:,1)

v3 = 3×1

-0.00146679475269089 -0.00264307281555424 -0.00329585789213623

Answer 1

[Christine Tobler]

The results look correct to me, can you say what you are expecting instead? Two points that are maybe relevant:

• MATLAB does numerical computation, so a round-off error compared to analytical computation is expected.
• The result of EIG doesn't give the eigenvalues in any particular order, so you may need to call sort on the eigenvalues and then reorder the eigenvectors accordingly.