Frequency Domain Analysis

Frequency Domain Analysis

In a frequency domain analysis, you study the response to a harmonic steady state excitation for certain frequencies. Such a steady state can prevail once all transient effects have been damped out.

The response must be linear, so that the single frequency harmonic excitation gives a pure harmonic response with the same frequency. The model may however contain nonlinearities; the harmonic response is computed around a linearization point. In such a case, the frequency domain analysis can be considered as a very small perturbation around the linearization point.


	Harmonic Perturbation

All loads and responses are in general complex valued quantities. If not all loads have the same phase, you can prescribe the phase of a certain in two ways:

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Add a Phase subnode to the load, in which you give the phase angle.

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Enter the load as a complex value, for example as
100[N]*(1+0.5*i)/sqrt(1.25).

Most results of a frequency domain analysis are complex. In results evaluation, the real value of any result quantity will be shown. Assuming that you want to display for example the displacement in the x-direction, u, you have following options:

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Plot u or real(u). This gives the displacement at zero phase angle.

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Plot imag(u). This gives the displacement at a phase angle of 90 degrees.

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Plot abs(u). This gives the amplitude of the displacement.

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Plot arg(u). This gives the phase angle of the displacement.

The reference phase, with respect to which the results above are reported.

Result quantities that are nonlinear in terms of the displacements, such as principal stresses, should be interpreted with great care. They will in general not be harmonic, so the amplitude and phase information is not reliable.

Some extra variables for postprocessing are created in a frequency-domain analysis. As an example, in the Solid Mechanics interface the following variables are defined:

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solid.disp—Norm of displacement (at current phase angle)

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solid.vel—Norm of velocity (at current phase angle)

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solid.acc—Norm of acceleration (at current phase angle)

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solid.disp_rms—RMS displacement over a cycle

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solid.vel_rms—RMS velocity over a cycle

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solid.acc_rms—RMS acceleration over a cycle

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solid.uAmpX—Amplitude of displacement in X direction

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solid.uAmp_tX—Amplitude of velocity in X direction

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solid.uAmp_ttX—Amplitude of acceleration in X direction

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solid.uPhaseX—Phase of X displacement, in radians

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solid.uPhase_tX—Phase of X velocity, in radians

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colid.uPhase_ttX—Phase of X displacement, in radians

The components in other coordinate directions are obtained by replacing X by another coordinate name.

Prestressed Analysis

The shift in the natural frequencies in a prestressed structure may have a significant effect on the frequency response. This is particularly important when the frequencies of the load are close to any of the natural frequencies of the structure. The Prestressed Analysis, Frequency Domain study type is designed to take such effects into account.

The prestress loading can include a contact analysis, in which case the subsequent frequency domain analysis provide as linearization around the current contact state.

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Prestressed Structures

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Harmonic Perturbation

Obtaining a Time History

Sometimes you want to study the time history over a period for the results of a frequency domain analysis. You can do that by adding a Frequency to Time FFT study step. The frequency response results are then viewed as terms in a Fourier series, which can be transformed to time domain. It is possible combine the results for several frequencies into a single time history, under the assumption that they are all multiples of the same fundamental frequency.

For an examples showing how to obtain a time history from frequency domain results, see

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Viscoelastic Structural Damper: Application Library path .

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Vibration Analysis of a Deep Beam: Application Library path .