Cantilever Beam Uniform Mass Natural Freq

  • Thread starter NeroBlade
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Hello

For my dynamics I had been going through some examples and verifying them using Staad Pro. However, I been having issues with some of the examples as some do not show the full detail of calculation description.

The one example been having problem with is where you must calculate the first 3 natural frequencies of the cantilever thats split up into 20 members with a uniform weight of 1.124lb per inch. Using the reference mentioned I assume the equation that is being used is the following:

[itex]\omega_i = 2 * \sqrt{\frac{AEN^2}{ML}} * sin(\frac{(2i - 1) * \pi}{4 N})[\itex]

Assuming
N = 20
L = 80 in
w = 1.124 lb/in
A = 4 in^2
I = 1.33333 in4
g = 386.4 in/sec2
E 30000ksi

M = (1.124/386.4) * 80

According to the example and the staad solution the 3 frequencies are as follows:



f1 = 10.237

f2 = 63.974

f3 = 178.67

Is it possible that you could clarify/correct my approach because I'm still having trouble obtaining these answers.
 

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