At 11:19 AM 8/10/2003 +0200, Jiri Sanda wrote:
>To later responses.
>Jan - I would like to see some designs that DOES NOT vibrate at all. Until
>now I have not seen such a beast !!!
Any round element will vibrate in the wind...simple mechanics and
aerodynamics (shed vortices), and forms the basis of such things as aeolian
harps. The vibration might not be noticable, or it might be quite
significant, and in a high Q system (which many mechanical systems are) the
vibration might build up to a significant amplitude.
This is a classic fluid mechanics problem...
f = S*U/D
f = frequency in Hz
S = Strouhal number (function of Reynolds number and cross section
U = velocity in m/sec
D = diameter in meters
Anything in aerodynamics is going to have something related to Reynolds
numbers, so it's worthwhile to compute it so we know what regime we're in.
Re = Reynolds number = U*D/nu
U = velocity
D = Characteristic length (diameter of tubing in this case)
nu = fluid kinematic viscosity: 1.51E-5 m^2/sec @ 20C
Say you've got a 2" diameter element (0.05 meters) in a 20 m/sec (45
Re = 20 * .05 / 1.51E-5 ... Re= 66E3 (scaling with size and wind speed..)
It looks like we're in the big medium Re regime (1000 to 1 million)
For 1E3<Re<1E6, S is typically in range 0.2 to 0.3,
so, for the same 2" tube in a 45 mi/hr wind, the vortex shedding frequency
f = .2 * 20 / 0.05 = 80 to 120 Hz
Make the tube bigger and the frequency drops, slow the wind down, and the
All you can do is try to design to minimize the displacement: stiff
members, make sure resonant frequency isn't at the vortex shedding
frequency, make sure that you don't have multiple coupled resonators, etc.
1) Multiple sizes of tubing. The driving frequency is determined to a
certain extent by the diameter of the cylinder, so, by using
tapered/stepped elements, you have less of the element trying to vibrate at
the same frequency.
2) Choose stiffness/mass/damping such that the element is not mechanically
resonant at a frequency which the aerodynamic forces will excite. (the rope
inside the tube approach is a combination of mass (reducing resonant
frequency) and damping (killing the Q of any resonance that is
there)). Most antenna design programs design for stiffness only (max
droop, and yield point)
3) Use non circular cross section tubing (which may be better or worse,
depending... aerodynamic analysis would tell)
4) Put resonance killers on the element (like those triangular things you
see hanging on power lines)... they disrupt the aerodynamics to keep the
lines from "galloping"
5) Put something along the surface of the tubing that breaks up the flow,
preventing the thing from shedding one giant vortex all at the same
time. Perhaps something as simple as pieces of wire or plastic strip glued
on in irregular intervals is sufficient.
>To kill the vibration with some rope or wire is fairly easy and does not
>represent any significant cost or problem to put in.