
Post by Br. Marius on Mar 31, 2015 13:26:33 GMT
(a) Identification of eigenroots with Floquet solution is a challenge (why?)
(b) High vibratory amplitude in the blade does not mean high dynamic stresses in the blade. Why so?
(c) The rotor acts as a big filter to suppress many harmonics of vibratory loads in the rotating frame to the fixed frame.
(d) A low frequency regressive flap mode becomes progressive mode at a high altitude.
(e) Constant coefficient approximation may be adequate in the fixed frame for an advance ratio of less than 0.3



Post by Br. Marius on Apr 1, 2015 18:56:14 GMT
(a) The eigenroots ρ of the Floquet transition matrix (central to developing the Floquet solution) are found via Equation 1 where λ represents the eigenvalues of A in a firstorderform expression of a forced vibration.
\(\rho=e^{[\lambda+\frac{2m\pi}{T}i]T}\)
However, the integer m is arbitrary and can only be found as it applies to a given flight condition via approximation. One method involves an iterative solution, starting from the hover condition where m can be computed directly and then using that solution to develop successive forward flight solutions. Another method involves transforming the solution to the fixed frame and neglecting all periodic terms. This assumption allows m to be computed directly.
(b) A high vibratory amplitude could be indicative of a blade with a low stiffness. Hence, large amplitudes would not necessitate high dynamic stresses.
(c) The rotor system is made to damp certain frequencies hence filtering what vibratory loads are observed by the hub.
(d) At high altitude, the decrease in air density decreases the aerodynamic forces on the aircraft. Hence, the aerodynamic damping decreases and the damped rotating flap frequency increases, allowing a regressive mode to change into a progressive mode.
(e) Constant coefficient approximation neglects periodic terms, which, in the Floquet solution to the eigenvalues of a rotor system in forward flight, are few. At advance ratios of less than 0.3, the system may be sufficiently axisymmetric in order to justify neglecting these terms as their relative size may be small compared to the constant terms.



Post by matthorr on Apr 5, 2015 4:21:10 GMT
Br. Marius, where did you find the info for part (e)? In the notes at the end of 2.10 he talks about \(\mu\) terms being constant but I don't see that in the equations.



Post by Br. Marius on Apr 5, 2015 19:49:32 GMT
Really, I didn't find much any information so I inferred that it might be a source of error in the equations. Did you find something to support an answer?



Post by matthorr on Apr 6, 2015 11:37:37 GMT
No, I didn't find anything. I think it is interesting that his notes say you get constant coefficients for \(\mu\) after doing the MCT, but the equations still have trig functions. It's probably an ordering scheme issue  at about \(\mu \geq 0.3\) you can't ignore the periodic terms anymore as they are of the same order as the rest of the terms.



Post by Br. Marius on Apr 6, 2015 13:50:57 GMT
That would be all that I see. Anyone else have input on this?

