The equilibrium equation for a structure
performing free vibration appears as the eigenvalue problem:
[K-λM]x
= 0
where
K is the stiffness matrix of the structure and M is the mass
matrix. Damping is neglected. The solution of the eigenvalue
problem yields n eigenvalues λ,
where n is the number of degrees of freedom. The vector x
is the eigenvector corresponding to the eigenvalue.
The eigenvalue problem is solved using a
matrix method called the Lanczos method. Not all eigenvalues are required
-- only a small number of the lowest eigenvalues are normally calculated.
The natural frequency fi follows directly from the eigenvalue λ.
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