Truss member resonance 1

[amorrison]

Helicopter design has a problem in that because of the different rotor rpms there is always a member in resonance somewhere in the structure.

In a new design there two options

1. As above - have all members at a different frequency with only one resonance occuring at one rotor rpm

or

2. Have all elements at one (or two or three?)frequency(s) and have the rotor pass through these frequencies quickly so no resonance damage occurs.

Any thoughts?

 

[MikeHalloran]

The typical rotor is too big to pass through any resonance 'quickly'.

Even if it could, the assumption that no damage would occur because there would be only a few cycles of resonance is not supportable for case 2. I'll expand on that a little:

At resonance, a truss member that is ordinarily a straight column is laterally deflected, i.e., bent, by its resonant response. It is therefore no longer sufficiently axially stiff to carry its normal share of the load. If other members are not also resonating at the same time, the resonating member's load is, we implicitly assume, redistributed to those other members, slightly increasing the load on each one. Because of normal factor of safety assumptions, this does not usually cause a problem.

If, as in case 2, every member, or a large number of members, are in resonance, and not as stiff as they otherwise would be, you effectively have an entirely new structure, a truss made mostly from curved columns, and the few straight columns might not be able to withstand the now greater share of the load they are asked to support.

Case 2 certainly doesn't guarantee instant failure, but it represents an entirely new load case and structure that you would be expected to foresee, and analyze.




Mike Halloran
Pembroke Pines, FL, USA

 

[GregLocock]

Interesting, we have a similar problem on electric coiling fans. These are driven by PWM, so in theory we can match the fan speed to the load, for maximum efficiency and minimum noise.

In practice there are various resonances in the running range of the fan, and there is also a minium and maximum speed that is achievable. So, instead of a smooth curve of speed versus coolant temperature, you end up with 'forbidden' speeds, and eventually you end up with a series of inclined steps, rather than a ramp.

As to option 2, you can't, physically, tune all the members to the same frequency, independently. I suggest you look into the theory of harmonic vibration absorbers for a detailed explanation. The handwaving explanation is that if you have a system with a resonant frequency f1, and couple it to another system with the same frequency f1, then two new resonances will occur, split by the modal masses of the two original modes. You can have two members resonating at the same frequency, obviously, but you can't approach that by tuning each member independently.










Cheers

Greg Locock

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