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Hi Thomas,

Your question is quite interesting, and there is not a single short answer.

First, you must notice that the problem you describe may or may not be periodic at all depending on the selected frequencies. If the ratio between all pairs of frequencies is a rational number, then a periodic solution exists. The period may however be long when compared to the periods of the contributing loads.

In your case, the periods of the two loads are 1/9 s and 1/11 s. The whole process is however periodic with the period 1 s, so in order to evaluate the full solution you need to combine 9 cycles of the 9 Hz solution with 11 cycles of the 11 Hz solution. Clearly, this is nothing that can be done by a pure frequency domain approach.

What you need to do is to solve the harmonic problem for each of the constituent frequencies, and then combine the results in the time domain. An example of how that can be done (for two frequencies, but the principle is general) can be found in one of the studies in https://www.comsol.com/model/vibration-analysis-of-a-thick-beam-20301 .

If you are only interested in an upper bound to the response, you can skip looking at the result in time domain, and instead just sum the amplitudes of the result for all frequencies.

If the process is not is not truly periodic (say that you have the frequencies 1 Hz and sqrt(2) Hz), you can always get an acceptable accuracy by assuming periodicity, and for example setting the second frequency to 1.41 or 1.414. For each decimal you add, the period of the combined result becomes a factor of 10 larger.

Regards,
Henrik

Hi Henrik,

Thanks for this tip ! I looked into the example you proposed and located the study that correspond well to what you were explaining and what I am looking for (overimposed frequency responses, time wise). It's called "periodic forced vibration" if I understand right, the 3rd one in 4.

One thing I do not get though, is through which steps the frequency responses are calculated and overimposed before extracting the time response with Inverse Discrete Fourier Transform. It seems there is only one harmonic load and the other one is not harmonic but has its phase shifting as a function of frequency. I was trying to get one of the two frequency only to be applied (as to perfectly understand the process) but it does not seem to work. Time wise, I'm only able to get two frequencies, or none.

In a nutsheel: inside Step 1 : Frequency Domain, only Edge Load 2 is enabled (the one with the phase) and in Step 2: Frequency to Time FFT all loads are disabled, but still I'm getting two frequencies in the time visualization.

Would you be please kind enough as to explain what I'm not getting here?

Thanks in advance

Hi,

If you look at the settings for Step1: Frequency Domain you will see that the only active load in that study step is Edge Load 2.

It is not tagged as Harmonic Perturbation since that study step is not of the perturbation type. In that study, an 'ordinary' load is considered as harmonic. If you were to change to Linear perturbation in the solver settings (see screenshot), then the solver would respond to the Harmonic Perturbation tag. You can compare with Modal Solver 1 in the previous study, which uses Edge Load 1.

Regards,
Henrik

In case #2 you want to calculate the response when there are two sources (forces) acting at the same time at different frequencies.

IF THE SYSTEM IS LINEAR you can do this by calculating the response at the two frequencies and summing them in the time domain.

If the system is not linear- the most obvious approach is to perform two time dependent calculations with sinusoids as forcing functions. However the calculated response will include both the forced response and an initial transient. The transient may take a considerable time to die away in order for you to get the steady state response (if that IS what you want).