error in using eig built-in function

Hi all,

I run into an issue whrn using the 'eig'.

I have 2 matrcies, and need to find the eigenvalues of using eig function.

Any hints why I run into such an issue?

Thanks in advance.

code snippet including the k and m matrcies are attached.

clc; close all; clear all; 
ro = 2700; %kg/m^3
a = 4e-2; % 
b = 1e-2; 
c = 1; % same as L 
L = c; 
A = a* b; % cross section area 
E = 70e09; % Youngs' modulus 
I = (1/12)*(a*b^3)% second moment of area. NOT mass moment 

I = 3.3333e-09

% case study is; simply-supported (pined-pined) beam 
% lateral or transverse vibrations 
syms x 
n = 1 : 1 : 10;
gamma = n .* pi ./ L;  
% phi = sin(gamma.*x); 
for i = 1 : length(n)
    for j = 1 : length(n)
        phi(i) = sin((i*pi/L)*x);
        phi(j) = sin((j*pi/L)*x);
        m(i , j) = int(ro*A*phi(i)*phi(j), x, 0, L);
        k_RR_Lag(i , j) = int(E*I*(diff(phi(i), x, 2)*diff(phi(j), x, 2)), x, 0, L);
    end
end
[eig_vec, eig_val] = eig(k_RR_Lag, m);

Error using sym/eig
Too many input arguments.

% Sort eigenvectors and eigenvalues
[eig_val, idx] = sort(diag(eig_val));
eig_vec = eig_vec(:, idx);

% Display results
disp('Eigenvalues:');
disp(eig_val);

disp('Eigenvectors:');
disp(eig_vec);

[Alireza]

Thanksa lot. I got it (the outcome of k and m are not nue=meric values at first, so it is needed to convert them into numeric values (using 'double') then apply the 'eig' function. Or first initialize/preallocate them via zeros ...

Answer 1

[Walter Roberson]

Symbolic eig() does not support generalized eigenvalues.

[Walter Roberson]

format long g
clc; close all; clear all; 
ro = 2700; %kg/m^3
a = 4e-2; % 
b = 1e-2; 
c = 1; % same as L 
L = c; 
A = a* b; % cross section area 
E = 70e09; % Youngs' modulus 
I = (1/12)*(a*b^3)% second moment of area. NOT mass moment 

I = 
      3.33333333333333e-09

% case study is; simply-supported (pined-pined) beam 
% lateral or transverse vibrations 
syms x 
n = 1 : 1 : 10;
gamma = n .* pi ./ L;  
% phi = sin(gamma.*x); 
for i = 1 : length(n)
    for j = 1 : length(n)
        phi(i) = sin((i*pi/L)*x);
        phi(j) = sin((j*pi/L)*x);
        m(i , j) = int(ro*A*phi(i)*phi(j), x, 0, L);
        k_RR_Lag(i , j) = int(E*I*(diff(phi(i), x, 2)*diff(phi(j), x, 2)), x, 0, L);
    end
end
[eig_vec, eig_val] = eig(double(k_RR_Lag), double(m));

% Sort eigenvectors and eigenvalues
[eig_val, idx] = sort(diag(eig_val));
eig_vec = eig_vec(:, idx);

% Display results
disp('Eigenvalues:');

Eigenvalues:

disp(eig_val);

          21045.1739888277
          336722.783821243
          1704659.09309504
          5387564.54113989
          13153233.7430173
          27274545.4895207
          50529462.7471753
          86201032.6582382
          138077386.540698
          210451739.888277

disp('Eigenvectors:');

Eigenvectors:

disp(eig_vec);

  Columns 1 through 7

          1.36082763487954                         0                         0                         0                         0                         0                         0
                         0          1.36082763487954                         0                         0                         0                         0                         0
                         0                         0          1.36082763487954                         0                         0                         0                         0
                         0                         0                         0          1.36082763487954                         0                         0                         0
                         0                         0                         0                         0          1.36082763487954                         0                         0
                         0                         0                         0                         0                         0          1.36082763487954                         0
                         0                         0                         0                         0                         0                         0          1.36082763487954
                         0                         0                         0                         0                         0                         0                         0
                         0                         0                         0                         0                         0                         0                         0
                         0                         0                         0                         0                         0                         0                         0

  Columns 8 through 10

                         0                         0                         0
                         0                         0                         0
                         0                         0                         0
                         0                         0                         0
                         0                         0                         0
                         0                         0                         0
                         0                         0                         0
          1.36082763487954                         0                         0
                         0          1.36082763487954                         0
                         0                         0          1.36082763487954

Answer 2

[Dyuman Joshi]

The symbolic function eig does not support the syntax that you are trying to use.

The numeric function eig does.

So, you can convert the variables to a numeric data type, preferrably by using double() .

Or you can preallocate them as a double array, as the values will then be automatically stored as double() values -

ro = 2700; %kg/m^3
a = 4e-2; % 
b = 1e-2; 
c = 1; % same as L 
L = c; 
A = a* b; % cross section area 
E = 70e09; % Youngs' modulus 
I = (1/12)*(a*b^3); % second moment of area. NOT mass moment 
% case study is; simply-supported (pined-pined) beam 
% lateral or transverse vibrations 
syms x 
n = 1 : 1 : 10;
gamma = n .* pi ./ L;  

num = numel(n);

%% Preallocate a double() array 
m = zeros(num);
k_RR_Lag = zeros(num);


for i = 1 : length(n)
    for j = 1 : length(n)
        phii = sin((i*pi/L)*x);
        phij = sin((j*pi/L)*x);
        m(i , j) = int(ro*A*phii*phij, x, 0, L);
        k_RR_Lag(i , j) = int(E*I*(diff(phii, x, 2)*diff(phij, x, 2)), x, 0, L);
    end
end

[eig_vec, eig_val] = eig(k_RR_Lag, m);

% Sort eigenvectors and eigenvalues
[eig_val, idx] = sort(diag(eig_val));
eig_vec = eig_vec(:, idx);

% Display results
disp('Eigenvalues:');

Eigenvalues:

disp(eig_val);

   1.0e+08 *

    0.0002
    0.0034
    0.0170
    0.0539
    0.1315
    0.2727
    0.5053
    0.8620
    1.3808
    2.1045

disp('Eigenvectors:');

Eigenvectors:

disp(eig_vec);

    1.3608         0         0         0         0         0         0         0         0         0
         0    1.3608         0         0         0         0         0         0         0         0
         0         0    1.3608         0         0         0         0         0         0         0
         0         0         0    1.3608         0         0         0         0         0         0
         0         0         0         0    1.3608         0         0         0         0         0
         0         0         0         0         0    1.3608         0         0         0         0
         0         0         0         0         0         0    1.3608         0         0         0
         0         0         0         0         0         0         0    1.3608         0         0
         0         0         0         0         0         0         0         0    1.3608         0
         0         0         0         0         0         0         0         0         0    1.3608