Resonance frequency of cantilever beam

AI Thread Summary
The discussion revolves around calculating the resonance frequency of a cantilever beam with specific dimensions and material properties. The user is confused by the significant discrepancy in results when using imperial units (14.74 Hz) versus SI units (289.6 Hz). They correctly converted the beam's specifications to SI but are unsure how to incorporate gravitational acceleration (g = 386 in/s²) into their calculations. The user notes that multiplying the imperial result by the square root of 386 yields a frequency closer to the SI result (262 Hz). The conversation highlights the importance of consistent unit usage and the role of gravitational factors in resonance frequency calculations.
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Homework Statement


Sorry for wasting your time and bandwidth, but I can't figure this out. I just have a cantilever beam with the following specifications:

length : 40 in.
width: 2 in.
height: 2 in.
E = 30e6 psi.
mbar = .8991 lbm/in.

And I'm trying to find the beam's resonance frequency (first mode). The problem is, I can't get a consistent answer between using SI units and the disastrous units given above.



Homework Equations



First I converted all of the above values to SI:

length = 1.016 m
width = .0508 m
height = .0508 m
E = 2.068e11 Pa
mbar = 15.878 kg/m

And I'm using the equation below to calculate the resonance frequency.

\omega = (1.875)^2 \sqrt{\frac{EI}{\overline{m}l^4}}}

where

I = \frac{wh^3}{12}


The Attempt at a Solution



If i do this, I get about 14.74 Hz for the imperial figures, and 289.6 Hz for the SI case. What gives? I have to be doing something wrong...
 
Last edited:
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g = 386 in / s^2 seems to be missing
 
How would that factor come about? I hvae converted all the imperial quantities as mentioned above, not sure where that factor would come in.

However, if I multiply my imperial figure by sqrt(386), I get about 262 Hz, which is somewhat close...

Thanks for your reply btw
 
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