# Resonant Frequency of a Cantilever

1. Nov 30, 2008

### mistry

Hi

I'm currently setting up a simple cantilever beam experiment. The cantilever will be positioned vertical and a spray force will be exerted from the left hand side, causing the plate to deflect. This deflection will be measured and recorded.

My question is how do I calculate the resonant frequency of this cantilever? I need to make sure that the force exerted does not cause the plate to oscillate at its resonant frequency and hence output inaccurate displacement values. If I can find this out I could possible determine an adequate thickness and length before making it.

Similarly, the force exerted will be from a spray. Is there a way of calculating the resonant frequency of the spray on the plate, to ensure I do not reach this point and hence obtain inaccurate values.

Mistry

2. Dec 4, 2008

### stewartcs

The natural frequency of a cantilevered uniform beam (with negligible beam weight) with a load on the free end is given by:

$$f_1 = \frac{\sqrt{3}}{2\pi}\sqrt{\frac{EIg}{Wl^3}}$$

Not sure on this part. However, what you might do is determine the reaction force of the spray impinging on the beam and then use that to get your theoretical deflection. It may give you some idea as to whether or not your results are skewed by resonance.

Hope this helps.

CS

3. Dec 4, 2008

### FredGarvin

The spray itself will not have a resonant frequency. Only bodies have a resonance (in this sense of the word). The spray will act as, most likely, a constant distributed force. In the worst case it would be a periodic force of some kind that would then be a forcing function. So your concerns of resonance will center around the frequencies you calculate for the beam and hope your spray's frequency (if there is one) doesn't coincide with one of the beam's modes.

4. Dec 6, 2008

### mistry

Hi

Thanks for your responses. In order for me to look into this further, 'stewartcs', can you tell me where you got the equation from or from which book?

Thanks

5. Dec 6, 2008

### stewartcs

Any vibrations book will have that equation in it (or even a strength of materials book). That equation was specifically from Roarks Stress and Strain.

CS