Cantilever Beam Uniform Mass Natural Freq

[NeroBlade]

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 that's 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.

 

[Achy47]

Hello,

Thank you for sharing your experience with using Staad Pro to verify your dynamics examples. It can definitely be frustrating when the calculations do not match up with the expected results.

Based on the information you have provided, it seems like you have correctly applied the equation for the natural frequencies of a cantilever beam. However, there are a few things that could be causing the discrepancy between your calculated frequencies and the ones provided in the example.

Firstly, it is important to ensure that all units are consistent in your calculations. In your equation, you have used inches for length and lb for weight, but then you have used 30000 ksi for the modulus of elasticity. This value is typically given in psi, so you may need to convert it to the same units as the other parameters in your equation.

Additionally, the value for the moment of inertia (I) that you have used is for a solid rectangular cross-section, but the example may be using a different cross-section. Make sure that the moment of inertia you are using matches the cross-section of the cantilever beam in the example.

Lastly, double check your inputs in Staad Pro to ensure they are accurate. Sometimes small errors in input values can lead to large discrepancies in results.

I hope this helps clarify your approach and leads you to the correct results. If you continue to have trouble, don't hesitate to reach out for further assistance. Best of luck with your dynamics studies!