# Modal analysis

The **modal analysis** includes experimental or numerical characterization of the dynamic behavior of oscillatory systems with the help of their natural vibration sizes (modal parameters) natural frequency , mode shape , modal mass and modal damping. In contrast, the vibration behavior in a certain operating state is recorded by the operating vibration analysis.

## Mechanics / acoustics

Similar to how a tuning fork vibrates at a certain frequency when it is struck, other objects, e.g. B. in technology, are set in their natural vibrations. The here z. Natural vibration quantities excited, for example, in bridges, drilling rigs, engine housings or aircraft wings represent global system properties. Knowledge of them enables a simple description and calculation of the dynamic system behavior.

To determine the modal parameters, the structure to be examined (the component to be examined ) is excited with a suitable excitation source (impact hammer, electrodynamic or hydraulic shaker ), with the exciting force usually being measured with a piezoelectric force transducer. At the same time, the structural responses are recorded with accelerometers or laser vibrometers . The frequency responses between excitation and response (see also response spectrum ) are then calculated using fast Fourier transformation (FFT) .

With common software packages, the eigenmodes of the examined system can be graphically animated. Operational critical or acoustically unfavorable natural vibration forms of the structure can thereby be discovered. Through targeted changes to the system properties, for example the material damping or additional stiffening measures, these can be changed in such a way that critical frequency ranges are avoided or driven through with a reduced amplitude.

Modal analysis is an experimental, analytical process in engineering that is often used to validate numerical processes ( FEM , also in connection with BEM ).

## Electrodynamics

Another application of modal analysis is the determination of which electromagnetic waves are propagating in a medium that is limited by conductive structures of any geometry (e.g. waveguide , TEM cell ). The propagation of a plane wave is often desired, but the geometry also enables other waves to be formed with electrical or magnetic components in the direction of propagation, as well as waves whose frequency is an integral multiple.

## literature

- DJ Ewins:
*Modal Testing: Theory, Practice and Application*. Baldock: Research Studies Press, 2nd edition 2003, ISBN 0-86380-218-4 -
Hans Günther Natke :
*Introduction to the theory and practice of time series and modal analysis - identification of oscillating elastomechanical systems.*2nd edition 1988, 3rd edition 1992, ISBN 3-528-18145-1 -
Horst Irretier :
*Modal analysis 1 and 2*, 4th edition, University of Kassel, Institute for Mechanics - Jimin He and Zhi-Fang Fu:
*Modal Analysis*. Butterworth-Heinemann, Oxford 2001, ISBN 0-7506-5079-6