Best way to experimentally find resonant frequency of thin beam?

[BofKGB]

Wondering how to go about finding the resonant frequency of a 200mm x 25mm beam with thickness equal to 2.5 mm. I am trying to get young's modulus by finding the resonant frequency. Thanks.

 

[NickE]

Put it on an e-mag shaker (as a cantilever beam), adjust the input frequency until the beam begins to flap wildly.

You could also try and get it to ring. support it at some f/n distance from either end and tap it lightly. Take an audio recording of the result. Spectrum analyze.

nick

 

[BofKGB]

Thanks Nick, I just want to make sure that however i fix the beam it doesn't effect it any.

 

[NickE]

To avoid altering the Fn (Thats frequency sub n) (or first fundamental) you can support at the anti nodes. They will occur at some n-number of places along the length of the beam. You will know them by the fact that the part wont move or vibrate while ringing. Much like a guitar string will make a harmonic when held lightly (not fretted just stopped) at the 5th or 7th or 12th fret. If you fix in the exact middle of the span and then ring IIRC this will give you the frequency one octave up from the fundamental.


(I'm curious as to why you need to experimentally determine the modulus. Is this a composite beam? If its a metal then likely someone has already determined the modulus and you should be able to use that. If you can empirically determine a modulus then I would check it with a published value to determine if its reasonable.)

 

[JStephen]

Normally, in the analysis of beams, you assume that the material in the beam is free to expand laterally. Due to Poisson's effect, the compression flange gets wider and the tension flange gets narrower.

However, when a flat bar bends the easy way, the tension part and the compression part are attached together, and you get lateral stresses that are not normally included in the beam design. The net result is that the bar is stiffer than the beam equations indicate. If I remember right, it is a factor (1-mu^2) or about 9% difference.

I mention this because I think the same effect will be present in your test, and might throw your results off somewhat.

As far as determining the modulus, it would probably work better to measure deflection versus load, with the beam loaded as a simple span or cantilever.

If this is by chance a college lab class, you may have access to microphones, strain gauges, oscilloscopes, or other goodies that would make measuring the frequency easy.

You can slow the oscillation down by adding a weight to the bar, if that would help. It would help if the bar were longer, so that frequency was low enough to count.

You can also use a strobe-type tachometer. I remember using one of those once, and the pitfall is that you can't distinguish a frequency from one that is double or triple.

 

[GregLocock]

Find a source of soft elastic bands. Hang the strip by one end from a few of these in series such that the suspension frequency is less than 2 Hz (say).

The strip is now free-free for all practical purposes.

To get good masurements from such a light system you'll find it dffiicult with a shaker, unless you use a piece of thread as the stinger. Even then the mass of the load cell is likely to compromise your result. You can make a very light impact hammer by strain gauging the shaft of a small hammer, or using a tiny load cell on its tip.

Since you are only interested in the frequency then you don't really need a load cell at all, you can just strike it with a suitable implement, and then pick the fundamental frequency up with a mic or other non contacting transducer.

You will get more reliable but less accurate results by using an accelerometer. To estimate the effect that your accelerometer is having on the result, put another one alongside, and then a third. This will allow you to estimate the trend of the change in frequency as parasitic mass is added.

Be aware of the nodes. If you strike the beam at a node then that frequency will not be excited. It is safest to srike and measure the repsonse at one end of a beam, since in free-free the ends are never nodal. the fundamental will be antinodal at the middle, so if you are only interested in that, use the middle.

Have fun, even a simple test like this will have gotcha's.





Cheers

Greg Locock

 

[JStephen]

"mu" up above should have been "nu", meaning Poisson's ratio.

 

[Tobalcane]

Just a question, why are you trying to find young’s modulus by frequency? Is the material unknown to you? Can you get a small piece and do a pull test? Unless using vibration is a standard way of finding the young’s modulus of metals?

Go Mechanical Engineering
Tobalcane

 

[GregLocock]

This is a standard method in the noise and vibration world, since you can also measure the damping of the material at the same time.

Cheers

Greg Locock