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Post by Br. Marius on Apr 10, 2015 17:40:52 GMT
Derive governing equations for flap bending and lag bending and then reduce these for a case of rigid rotor with offset hinges.
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Post by Br. Marius on Apr 11, 2015 1:35:46 GMT
Maybe this is a dumb question, but what is he asking here? Is he asking for the simple flag/lag equations we derived at the beginning of the course? Or the coupled flap-lag equations we did a couple chapters ago? Is he asking for the perturbation equations in flap and lag (which he asks for in question 4)? And, in all of these, the derivation starts with an assumption concerning whether or not the rotor is treated elastically or as a rigid blade on an offset hinge...it doesn't end with it. What's going on with this question?
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Post by trdodge on Apr 11, 2015 23:57:52 GMT
I just looked up flap bending and lag bending in the index of the book, there's a nice little section on each of them where the equations are derived (page 592 and 603, respectively for the 2013 version), and it's pretty much verbatim what we've done in class before (with the AF, CF, and IF forces). They then include beam theory M = EI*w'' and derive the rotor blade bending equations.
I think what he's looking for is the derivation of these equations, then make the assumption that we have a root spring at offset e (EIw'' = Kb*w' at r=e) as the boundary conditions. That's what I had been playing around with, will let you know if it seems reasonable.
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Post by Br. Marius on Apr 12, 2015 13:14:41 GMT
Could you post a copy of the 2013 book (if you have it in electronic format)? It doesn't look like that made the cut for the 2015 edition.
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Post by trdodge on Apr 12, 2015 16:53:12 GMT
I'm sorry it's a hard copy of the book. The chapter and section was 16.3 Out of plane motion, if that's helpful at all. For what it's worth after playing with it I'm not convinced I'm going about it right.
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Post by Deleted on Apr 12, 2015 19:12:59 GMT
These are the sections from Johnsons book. I assume that was the reference mentioned. |
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Post by Deleted on Apr 12, 2015 19:16:46 GMT
I have an electronic textbook rental that is very proprietary for printing and it only allows 10 pages to be printed in specific time intervals. Please let me know if there are any other pages you want and I will attempt to post it.
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Post by matthorr on Apr 13, 2015 11:54:18 GMT
I think he's looking for us to use section 3.3.2 out of the notes - Flexible Model for flap and lag bending. At the end, he discusses boundary conditions for hingeless blades, we would have to replace @r = 0 with @r = e. I'm not sure how to "reduce these" since you can't just substitute in the B.C.s for a differential equation...
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