If you've been in the engineering world for any length of time, i'm sure you've heard the terms "buckling" and "resonant frequency" thrown around; you also may very well know what each of these terms mean, but have you ever thought of them being linked together?? I mean buckling has to do with compressive loading on thin, long members, and resonant frequency has to do with a structure's frequency at which it vibrates; what could these two possibly have in common?
The answer to this question lies within a phenomenon call Stress Stiffening. When a load is applied to a structure, the load will affect the frequency at which the structure vibrates. This is best seen in the case of a guitar string. When the guitar is tuned, the string is pulled tighter or looser in order to achieve the right tone. The tighter the string is pulled the higher the frequency it vibrates at and the higher pitched tone it makes.
This concept can be applied to other structures as well, not just guitar strings. When a load is applied in tension on a structure, it will cause it's natural frequency to go up. Like-wise, when a structure is loaded in compression, it's natural frequency will go down. You're probably thinking, so what? What does that have to do with buckling? Well in buckling, what really happens when a structure collapses is the structure loses it's stiffness and collapses or buckles on itself. If we look at the equation for natural frequency, we see that it is equal to the square root of the structures stiffness divided by it's mass. So now we know that based on this equation, when the stiffness goes to zero, so does the natural frequency! And thus we have our link between frequency and buckling! Let's take a look at a simple example to prove this concept out....
Below is a simple cylindrical pipe that is fixed on the bottom and carrying a compressive load. Using our buckling analysis in SOLIDWORKS Simulation, we can see the load that will cause this cylindrical pipe to buckle.
Now if we take this same load and run a Frequency study on it, we can see the resulting fundamental natural frequency is very close to zero, meaning that the stiffness of the structure is almost reduced to nothing!
I don't know about you, but it's cool for me when I come across some of these correlations between phenomenon we see in the engineering world!
By: Chris Olson, Simulation Applications Engineer
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