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In FEA, I have a complex system onto which I have applied some boundary conditions and then conducted a modal analysis for it. In return, I got a few mode shapes (as much as I requested) for each of the natural frequency from the FEA solver. By definition, a mode shape which is associated with a certain natural frequency is the deformed pattern of a system at which it will vibrate at that natural frequency. A system will have as number of natural frequencies (and thus the mode shapes) as the number of DOFs in the system (basically the total number of DOFs of all the nodes in my Finite Element model).

Now, I want to understand that how can I achieve this mode shape in reality? I mean a natural frequency by definition is the frequency at which the system will vibrate when subjected to disturbance, and without any action of continous force. So how should I disturb my system in order to make the structure vibrate at a specific natural frequency with a certain mode shape?

And in what way should the external excitation frequency be applied onto the structure in order to obtain a certain mode shape?

Plus, is it possible to get more than one mode shape for a specific natural frequency? Or is it possible to see more than one natural frequency for the same mode shape?

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  • $\begingroup$ Examples... Imagine a long bar of rigid material. Strike it through the CM along the long side and you get a bending vibration. Strike it at the end, instead, and it gets a longitudinal vibration. Strike it off of center along the long side, instead, and you get a complex result. $\endgroup$
    – Jim Clark
    Jan 12, 2022 at 14:15

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For a cantilever beam, we can either add point mass or initial constrains, encouraging the beam into the desired mode shape.

In most of the vibrations, all modes will emerge given enough time. The dominant modes and those with higher mass participation mask the high-frequency modes to some extend.

If we could record the vibration at high speed we can detect many modes superimposed on top of each other.

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In reality these mode shapes combined (superimposed) form a response (eg. receptance \alpha). See the plot below for a response of a single point. In the Figure you see the individual mode shape contributions. In black is the actual (combined) frequency response. Each mode has an eigenvalue (resonance) and eigenvector (mode shape - spatial response).

enter image description here

You can tell that at resonance the mode is prevailing, therefore if you measure the response at the resonant frequency you get a more than fair approximation of the mode.

For a different spatial point the graph would have the same resonant frequencies but the amplitudes of the modes would be different, due to the spatial aspect of the eigenvector. So if you plot the amplitudes of the responses for a given frequency but for different locations you see the spatial response - the operational deflection shape (ODS) at that frequency. Because modes prevail at the resonance the ODS at the resonant frequency is basically the mode shape.

You can see examples of this in this video: https://www.youtube.com/watch?v=9cPAjlDFxMI

To measure a response at a given frequency you have to excite that frequency. That can be done with a shaker (as in the video above) or for instance with a hit which excites a broad band of frequencies including the resonance.

Is it possible to have two modes at the same resonant frequency? Yes, this happens when you have symmetric structures and the symmetric modes share the resonance. Think of a square rod. It will have same bending modes in both axis of the rod thickness.

More than one resonance for the same shape? No, I don't see how that would happen.

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Now, I want to understand that how can I achieve this mode shape in reality? I mean a natural frequency by definition is the frequency at which the system will vibrate when subjected to disturbance, and without any action of continous force. So how should I disturb my system in order to make the structure vibrate at a specific natural frequency with a certain mode shape?

If you want to excite a mode apply an excitation to an antinode of that mode. You will get some excitation of the other modes unless they are nodal at the location and direction.

And in what way should the external excitation frequency be applied onto the structure in order to obtain a certain mode shape?

If you apply a single frequency excitation to the structure it will only respond at that frequency (if it is a linear system), so long as it is not at a nodal point (zero response)

Plus, is it possible to get more than one mode shape for a specific natural frequency? Or is it possible to see more than one natural frequency for the same mode shape?

No, and no, in a linear system.

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