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# Harmonic frequency analysis

Frequency response analysis falls within the field of dynamics under the structural-mechanical calculation methods of FEM. It is used to determine the response of a structure to a harmonic excitation in the stationary, i.e. steady state. If one goes by the type of excitation, the English term "Harmonic Frequency Response" is more appropriate. In contrast, the German name is based on the result of the simulation, in which the response behavior is determined for a certain frequency range of the excitation. The result is the amplitude and the phase angle as a function of the excitation frequency, the so-called phase frequency response or excitation frequency response.

The consideration takes place in principle in the frequency range. Changes in structural behavior due to non-linear effects cannot be taken into account, nor can loads acting on the structure at different frequencies. A change of excitation amplitude or excitation frequency is also not possible. If, from a technical point of view, the reactions to such load changes are to be considered, a transient dynamic analysis must be carried out. Damping, on the other hand, can be included in the system description in various ways.

## Computation time / model size

For a frequency response analysis different methods are available, which differ in the numerical effort and the possibilities to consider physical effects. The most common methods are the direct solution and the modal superposition. The approach of using the complete system matrices directly is the most intensive in terms of computing time, but also offers the more accurate results.

## Relevance

A frequency response analysis covers a widespread case of dynamic structural loading in technical applications. Machines and systems in particular often experience a stationary harmonic excitation that can be observed with this type of analysis.

Other influences such as Coriolis force, gyroscopic moments, stress stiffening and "spin softening" have to be taken into account when excitation is caused by unbalance or the impact of a fast-running shaft. This frequently occurring special case of harmonic excitation falls into the field of rotor dynamics.

Further special cases of frequency response analysis are the fluid-structure interaction or the self-excitation of a structure by friction effects.

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