What is the purpose of modal analysis?

[Trying2Learn]

TL;DR Summary

What is a "simple" and "intuitive" explanation of modal analysis for the public.

Hello all,

I have been asking this question, here, and gaining more insight. I think I can finally ask it the way I need.

I can:

• Conduct an eigenvalue analysis
• Code the Lanczos algorithm.
• Understand mode shapes
• Build the solution of set of coupled differential equations from mode shapes.
• Conduct a modal analysis on a finite element mesh.

All that is clear.

But if you were to ask me to explain what a modal analysis is to a person uninitiated in the math or engineering, I cannot do it.

If you were to, say, design an exhibit for a science museum, or write a book for the public, how would you explain modal analysis?

For example, this from wiki: "Modal analysis is the study of the dynamic properties of systems in the frequency domain. "

Yes, I understand that. But someone who is not a mathematician or an engineer, will not. Frequency domain, dynamic properties, yes, I get that. But it does not help me explain it to, say, my brother.

I can talk about soldiers marching over a bridge, having to break step, or the Bessel functions on the surface of a glass of water when a T-Rex is coming. But I am unable to explain what modal analysis is.

I am labeling this with an "Advanced" label, since I think this might need to be explained from the top, down.

(And, if possible, avoid any anthropomorphic explanation like: "the structure wants to do this...")

(It is almost as if I am looking for a philosophical explanation... I think...)

Can anyone help?(And even then, I would like an explanation for both discrete and continuous systems. Or is it possible that any explanation must drive down to the molecular level and discuss vibrations)

 

[jrmichler]

How about this:

If you shake or hit an object, it will vibrate at one or more frequencies. Modal analysis calculates the frequencies. The object can be a part, a bridge, an airplane, or a window in your house.

From there to the Millennium Bridge, aircraft wing flutter, or your window shaking when loud music hits the right frequency.

 

[DaveE]

Guitar strings and flutes. People with a musical background have heard of harmonics, use that as a basis for explaining that structures have characteristic (modal) responses. How do they tell a G string from an F string? By modal analysis in their brain. How do they tell if they are blowing too hard into their recorder? By modal analysis in their brain.

 

[anorlunda]

Here's a graphical depiction that the public can understand.

You could show how to create a square wave by adding one more harmonic at a time. You could do that with graphics, no math. Then, just say "analysts can do that backwards, starting with the square wave and finding the component harmonics.

 

[Trying2Learn]

Thank you everyone

These are all excellent ideas to deliver the idea.

If there are any more, I would be as appreciative.

 

[DaveE]

There's a whole bunch of great demos on YouTube, like this one, for example:

 

[Arjan82]

So this would be my way:

====
Take any object that you can apply modal analysis to, deform it a little bit (i.e. still linear elastic deformation) and let it go. It will obviously go back to it's un-deformed shape. How fast it will do that depends on two things: its stiffness (i.e. resistance to deformation) and its mass (inertia). The stiffer the faster the return to 'normal' and the more mass the slower the return to normal.

When arriving at its un-deformed shape, the object will have a velocity however and thus move past this shape and deform in exactly opposite direction until the stiffness of the object prevents it to go any further, and indeed it will move the object back once again.

This means the object is now vibrating around its un-deformed shape with a certain frequency which depends on its mass and stiffness. Modal analysis is the analysis to find this frequency.
====

Depending on the level of the listener you could continue to say that there are actually more than one frequency with each their own mode shape (actually theoretically infinite for continuous media), that any linear deformation of the object can be described as a superposition of its mode-shapes etc.

The tricky bit is to intuitively explain why a particular shape is a mode shape and why other shapes are not mode shapes. I think it has something to do with the more or less even distribution of deformation energy or something like that, but that is where my knowledge ends :).

 

[anorlunda]

You can do better than that. Below is a depiction of some different modes of vibration of a drum head. Nothing could be simpler than a drum.

 

[Arjan82]

How do they tell a G string from an F string? By modal analysis in their brain.

I kind off disagree with this explanation. A modal analysis solves for the frequencies, and this happens at the string itself 'by nature'. Then these vibrations are carried over via air, your eardrum, and nerves to your brain. Your brain interprets soundwaves, it doesn't do modal analysis.