how to find eigenvalues using the determinant ?

Hello,

I have mass and stiffness matrices and i want to find the eigenfrequency using det(K-w^2*M)=0 while K and M are the matrices and w is the eigenvfrequencies.How can i change this equation into mode and getting w ?

Answer 1

[Christine Tobler]

The determinant should only be used explicitly to solve an eigenvalue problem for symbolic calculation (for example, when you solve a 2-by-2 problem by hand). In numeric computations, the determinant is not robust and not advised to use.

You can compute the eigenvalues and eigenvectors using the EIG function, [V, D] = eig(K, M). This gives you eigenvalues (diagonal of D) and eigenvectors (columns of V) of this problem. The matrices satisfy

norm(K*V-M*V*D) % == 0 up to round-off error

To get the w value you want, you simply take the square root of the eigenvalues, sqrt(diag(D)).

Answer 2

[John D'Errico]

This is a generalized eigenvalue problem. READ THE HELP FOR EIG. If you pass in both matrices, it still computes the eigenvalues.

Do you want to use the determinant? NO! Learn to use eig.