## L. Modal Analysis of a Periodic Elastic Structure (MOD6)

In this analysis, only the displacement field is relevantand the loading vector is set to zero. Only a two-dimensional or three-dimensionalcell of the elastic structure is meshed. The user specifies the wave vector,i.e., the wave number and the direction of propagation of the acoustic wave, aswell as the faces of the elementary cell on which the Bloch-Floquet conditions are applied (see Section III.D, PERIODIC, ANGLES, WAVENUMBER entries). The system of equations is reduced to:

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

where the stiffness and mass matrices have been modifiedafter the assembly phase to take the specific implicit boundary conditions intoaccount. The code computes the real eigenvalues and complex eigenvectors ofthe linear hermitic system that are the characteristic frequencies and modes ofthe structure for the given wave number.

The matrices are assembled and stored to file by columns. Lanczos' algorithm for hermitic matrices is used to solve the problem. Theproblem can be solved only in double precision.