Best way to experimentally find resonant frequency of thin beam?
Best way to experimentally find resonant frequency of thin beam?
(OP)
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.





RE: Best way to experimentally find resonant frequency of thin beam?
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
RE: Best way to experimentally find resonant frequency of thin beam?
RE: Best way to experimentally find resonant frequency of thin beam?
(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.)
RE: Best way to experimentally find resonant frequency of thin beam?
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.
RE: Best way to experimentally find resonant frequency of thin beam?
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
RE: Best way to experimentally find resonant frequency of thin beam?
RE: Best way to experimentally find resonant frequency of thin beam?
Go Mechanical Engineering
Tobalcane
RE: Best way to experimentally find resonant frequency of thin beam?
Cheers
Greg Locock