## I. Modal Analysis of a Magnetostrictive Structure (MOD3)

In this analysis, the system of equations is reduced to:

For different electrical boundary conditions, the codecomputes the eigenvalues and eigenvectors of the linear system that are thestructure's eigenvalues and eigenvectors. The computation is done using realvalues with no internal losses. Eigenvectors are normalized such that UT [M] U= 1, [M] acting for the meshed structure, that is including the axisymmetryfactor 2p for axisymmetric structures but notincluding symmetry factors induced by explicit boundary conditions.

The open-circuit modal analysis, obtained by taking I = 0, leads to the computation of the antiresonancemodes. The short-circuit modal analysis, obtained by taking fb = 0, leads to the computation of the resonance modes. Calculating the resonance and antiresonance modes can be carried out in onestep (see Section III.D, ANALYSIS entry). In this case the excitation currents are referenced in the EXCITATIONS entry.

The matrices are assembled and stored to file by columns. Lanczos' algorithm is used to solve the problem. It can be done only indouble-precision. It has to be noted that:

- The retained algorithm provides the rigid body modeswhen they exist

- This algorithm computes the eigenvalues very accuratelyeven when the resonance modes are very close or when there is anill-conditioned matrix.

Remark: The electrical degrees-of-freedom are placed at the beginning of the assembled matrix. The numerical system can differ in sizefrom a harmonic analysis. Also, any provided mechanical excitation will be treated as blocked.