## G. Modal Analysis of an Elastic Structure (MOD1)

In this analysis, only the displacement field is relevant and the loading vector is set to zero. The system of equations is reduced to:

([Kuu] - w2 [M]) U = 0

The code computes the eigenvalues and eigenvectors of thelinear system that are the characteristic frequencies and modes of thestructure. The computation is done using real values with no internal losses. Eigenvectors are normalized such that UT[M] U = 1, [M] acting for the meshedstructure, that is including the axisymmetry factor 2p for axisymmetric structures but not including symmetry factors induced byexplicit boundary conditions.

The matrices [Kuu] and [M] areassembled and stored to file by columns. Lanczos' algorithm is used to solve the problem. It can be solved only in double precision. It has to be notedthat:

- The retained algorithm provides the rigid body modes when they exist

- This algorithm computes the eigenvalues very accurately even when the resonance modes are very close or when there is an ill-conditioned matrix.