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Structures have infinite DOFs, so it possess infinite mode shapes. How can we find the right resonant frequency out of the infinite resonant frequencies so that we can save our structure?

For example, if we do vibration analysis in SOLIDWORKS, and we take the first 5 frequencies, it will give us 5 different shapes. In that case:

  • How can we make sure that our analysis is right?

  • Which frequency out of those five is right?

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Assuming that the model is adequate and appropriate, then to answer your second question:

Which frequency out of those five is right?

All of those modes and frequencies are possible in the structure. Usually the frequencies are provided in increasing order (i.e. the numerical smallest is presented first etc).

The frequency that is usually more important, are those that are closest to the excitation frequency. This is because eigen frequencies in the structure close to excitation frequency can cause resonance.

a note on "Right and wrong"

regarding the first question:

How can we make sure that our analysis is right?

I should point out that all the frequencies are "right" and at the same time "wrong".

They are

  • right because those are the eigenfrequencies that the SOLIDWORKS model has calculated numerically
  • wrong because the Solidworks model is an approximation of the structure and so you can't really rely on them.
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    $\begingroup$ I would a) check more eigen frequencies (close to the 100kHz) and b) consider the transient effects when starting from rest and going up to 100kHz. $\endgroup$
    – NMech
    Commented Dec 30, 2021 at 14:33
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    $\begingroup$ @Ibrahim Omer ... 100kHz is in the ultrasonic range, far from frequencies in structural applications. I would carefully check whether the structural analysis software is valid for such frequencies ... consider e.g. speed of sound in steel is on the order of 5000 m/s -> wavelength at 1kHz is 5m , wavelength at 10kHz is 50cm etc, wavelength at 100kHz is 5cm $\endgroup$
    – Pete W
    Commented Dec 30, 2021 at 16:37
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    $\begingroup$ @PeteW It was just an example, you can take frequencies in MHz. $\endgroup$
    – Ibrahim Omer
    Commented Dec 30, 2021 at 16:37
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    $\begingroup$ fyi MHz is even further away $\endgroup$
    – Pete W
    Commented Dec 30, 2021 at 16:38
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    $\begingroup$ @NMech Lets make it 15Hz (Structure). Now it will make sense. $\endgroup$
    – Ibrahim Omer
    Commented Dec 30, 2021 at 17:05
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It depends what you think should be the frequency of the external force, which will cause it to vibration. If the frequency of the external force is overlapping with any of the natural frequencies, then the structure resonates and you have high amplitude of vibration, which can catastrophically damage the structure.

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