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# Modal analysis

Modal analysis is the basic FEM calculation method in the field of dynamics. It is used to determine the natural frequencies and the natural modes of vibration of a structure. Both sizes always occur in pairs. The natural mode of vibration is the state of deformation that would result from excitation with the associated natural frequency. However, the calculated displacement values do not correspond to the actual oscillation amplitudes, but merely serve as a relative comparison between different positions on the structure.

The calculation method does not allow for non-linear effects. Changes in the contact state caused by a mode of vibration or local plastification of the structure are therefore not recorded. The simulation can be carried out for unstressed, clamped or prestressed systems. For the consideration of a pre-stressed structure, the stress condition for the clamping situation must first be determined with an upstream static FEM analysis.

The simulation can be carried out for undamped and damped structures. In the case of the damped system, this leads to asymmetric matrices that require other numerical solution algorithms. The solution results in complex eigenvalues and the overall calculation effort increases as a result.

## Computation time / model size

Regardless of this, the calculation time depends on the model size and the number of modes to be included in the technical evaluation. The disc space requirement for temporary calculation data and the storage of results is also increasing.

A significant performance gain can be achieved by dividing a large model into smaller, interlinked parts. If this splitting is done over several levels, the technique is called "Multi Level Dynamic Reduction". Some FEM programs offer special routines for this purpose, which automatically perform this subdivision and the sequential solving of the partial models up to the complete model.

## Relevance

The results of a modal analysis are essential for the assessment and dimensioning of dynamically loaded systems. Modal analysis therefore plays an important role. Besides static FEM simulation, it is certainly the most frequently used type of analysis in mechanics.

In addition, the result of modal analysis is used as a basis for further simulations. These include frequency response analysis, analysis of the response spectrum or the investigation of randomly excited oscillations using PSD analysis (Power Spectral Density). The dynamic reduction of a structure is also based on the results of modal analysis.

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