# PERMAS-DEV Dynamic Eigenvalues

The PERMAS-DEV (Dynamics/Eigenvalues) module provides for the calculation of real eigenvalues and mode shapes of the structure. The specification of a number of modes and an upper frequency limit is supported. The very efficient subspace iteration algorithm used is capable of solving very large eigenvalue problems. Rigid body modes are detected automatically or may be explicitly defined and are decoupled prior to the subspace iteration.

If the number of modes is increasing, one can observe a disproportional increase of solution time, because the last modes take more time than the first modes. Therefore, a shift method has been introduced which are used to split the frequency domain in several parts and to solve each part separately. Then, even the last modes can be solved as fast as the firstmodes resulting in an overall run time reduction for the complete analysis. The shift method is used automatically by PERMAS in cases where a large number of modes is required (> 5000 modes) or where the standard method takes a long time to converge. In addition, a higher accuracy of the mode shapes can be expected from this method.

The stiffness matrix can be modified taking into account additional stiffness effects:

- Geometric stiffness for any load,
- Centrifugal stiffness for rotating parts under constant rotational speed referring to co-rotating reference system,
- Convective stiffness for rotating parts under constant rotational speed referring to inertial reference system,
- Pressure stiffness for shell elements and fluidfilled pipe elements under pressure.

for the first 20 eigenmodes.

Additional tools are available for the further processing of modes:

- Modal stresses can be derived from modal displacements.
- In addition, modal potential and kinematic energies can be calculated and exported.
- For the evaluation of modes, e.g. with respect to local or global mode shapes, energy balances can be determined and exported for all sets in a structure.
- MAC (Modal Assurance Criterion) factors and other factors are available to compare modes between two different modal analyses
- As a measure for the completeness of the modal model, effective masses are generated and printed on the result file.

A generalized modal condensation is available to establish system matrices in modal space for external applications. Export of modal models is either supported by interfaces (e.g. to MBS systems) or by direct specification of the matrix items.