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PSD analysis

Power Spectral Density Analysis (PSD) is named after the way the excitation spectrum for the simulation is described, as auto- or active power spectrum. In addition to response spectrum and frequency response analysis, it is another method of FEM to investigate the response to a structural excitation. The excitation spectrum can be any random stochastic signal. Hence the second, frequently used term random response analysis.

If a structure is operated in the area of time or fatigue strength, the knowledge of the maximum load alone, as it can be determined, for example, with a response spectrum analysis, is not sufficient or too conservative for an assessment. For a damage prediction it is rather necessary to know the frequency and the magnitude with which individual amplitudes occur. This necessary information could theoretically all be determined with a transient analysis in the time domain. However, due to the complexity of the excitation signal, this would be a very time-consuming, inefficient approach.

Instead of determining the effects of individual vibration amplitudes, a power spectral density analysis captures the problem in the frequency domain using statistical methods. The result is the probability, expressed as a standard deviation, with which a certain structural response occurs. Together with the load duration and the associated frequencies, damage accumulation can be used to evaluate the fatigue strength of the structure.

Similar to the other simulation methods that use modal superposition, random response analysis does not allow nonlinearities.

Computation time / model size

Compared to the complexity of the task to be solved, PSD analysis requires little numerical effort. Since it is based on the results of modal analysis, however, the determination of the natural frequencies and eigenmodes must also be included in the total calculation time. Accordingly, the same considerations should be made with regard to model size as for modal analysis.


The Power Spectral Density Analysis currently provides the most realistic simulation results for structures that are exposed to a stochastic excitation spectrum. Accordingly, proof of a defined active power spectrum is often required in the specifications for a product.


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About us

AdSimuTec GmbH is a small, innovative engineering service provider specialized in the field of numerical simulation with FEM & CFD.

You will find us in Eastern Switzerland, more precisely in the Rhine Valley of St. Gallen. We are only a stone's throw away from Vorarlberg (Austria) and Lichtenstein on the one hand and Baden-Württemberg and Bavaria (Germany) on the other.