Eigenvalue problem, singular matrix

Hello everyone! I have a mass matrix M and a stiffness matrix K generated by FEM (ANSYS) imported to Matlab and I want to calculate the eigenfrequencies and natural modes of the corresponding structure. The matrices are sparse. I tried the command:

[U,V] = eigs(K,M)

but it only gives:

Error using eigs/checkInputs/LUfactorB (line 1001) B is singular. Unable to compute the specified eigenvalues because infinite eigenvalue(s) exist

When I specify, that I only want the 50 lowest frequencies:

[U,V] = eigs(K,M,50,'sm')

it works, although they seem suspiciously high. The problem is that it wasn't me who generated the FEM model and also that I have almost no experience in the field. But I thought that if the FEM model has n rigid body motion degrees of freedom, then the structure will have n zero natural frequencies. Here Matlab complains about the opposite, namely infinite frequencies. Please do you somebody see what is happening? Thank you! Jan

Answer 1

[Matt J]

Because your M matrix is singular, there are infinite eigenvalues. Imagine for example if M=zeros(n). Then any vector in null(K) is an eigenvector and any scalar is a corresponding eigenvalue. The bottom line is that you have bad 'M' data.

[Jan]

Not that it would take me two months to figure out, but yes, the data was indeed faulty. I just forgot to accept your answer. Thank you!