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Post by Br. Marius on Feb 19, 2015 15:09:53 GMT
The natural vibration characteristics of a rotating blade in pure torsion mode is obtained from the homogenous solution (forcing = 0) of the governing partial differential equation where GJ is torsional stiffness and Iθ is torsional inertial. The boundary conditions are defined as: zero deflection at the root (geometric b.c.) and torsion moment is zero at the free end (force b.c.).
Using Galerkin method, calculate approximately the fundamental torsion frequency of this uniform blade. Assume the one term deflection as given.
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Post by Br. Marius on Feb 19, 2015 19:49:31 GMT
So I am looking at the equation that he gave us for the assignment, and I'm trying to figure out, conceptually speaking, what influence the rotor's angular speed has on blade torsion. Any thoughts? What does this term represent?
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Post by Br. Marius on Feb 20, 2015 21:36:31 GMT
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Post by Br. Marius on Feb 23, 2015 13:59:56 GMT
I got \(\omega = \sqrt{\frac{\frac{GJ}{3R}+\frac{2}{15}I_{\theta}\Omega^2R}{\frac{2}{15}I_{\theta}R}}\). Work is attached. Attachments:Galerkin.pdf (589.58 KB)
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Post by Deleted on Feb 23, 2015 20:20:01 GMT
Hmmm close. I got \(\omega=\sqrt{\frac{\frac{GJ}{3R}+\frac{2}{15}I_{\theta}\Omega^2R}{\frac{2}{15}I_{\theta}R}}\)
It's hard to tell exactly where the difference is since we used different evaluation methods (I did a change of variables: x = r/R). So maybe we just have to recheck our work.
Good, same thing now!
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Post by Deleted on Feb 24, 2015 13:10:27 GMT
So I am looking at the equation that he gave us for the assignment, and I'm trying to figure out, conceptually speaking, what influence the rotor's angular speed has on blade torsion. Any thoughts? What does this term represent? Tried to give some thought to your question and at least in the free vibration the rotating and nonrotating modes are identical since torsional stiffness GJ is unaffected by rotational speed in given equation. I think that is what you observed and I said it differently. If I have time I will try and talk to the professor about it to get more insight. |
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Post by Br. Marius on Feb 24, 2015 14:20:05 GMT
It's appreciated--thanks!
Also, Justin, just found my mistake. I dropped an R during integration...all set now. Just need to finish up FEM now...isn't it nice how it's 3 times as long (as least for me) as the other two? Reminds me of ENAE684...
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