Question about the frequency of a flow induced vibration

[lynnds]

How do you predict or calculate the frequency of flow induced vibration of a polymer yarn? We produce carbon fiber from a multifilament polymer yarn. Part of this process is to entangle the multifilaments of polymer into a bundle. The yarn is passed through a small device with air holes that causes the yarn and filaments to vibrate and therefore entangle. I can calculate the natural frequency based on the yield (mass per length), tension, and span between the guide rollers; however, the actual frequency is usually higher than the natural frequency. I am a vibration novice at best.

 

[vanstoja]

If the individual strands or yarn have the cross-section of a right circular cylinder and the airflow is perpendicular to the cylinder axis, the wake shedding frequency is given by the so-called Strouhal equation, ie, f=Sv/d where v is flow velocity impinging on the cylinder, d is a characteristic dimension (in this case, the cylinder diameter) and S is the Strouhal Number which is equal to 0.19 to 0.21 over most of the flow Reynolds Number range.
As an example, for d=1/32 inch, v=20 ft/sec, S=0.20 the frequency is 1536 Hz.

 

[pja]

vanstoja's answer is correct if the vibration is not self-excited..ie a flutter type phenemenon which
is seen on lifting surfaces but also has been observed
in paper mills where paper is run through rollers which have air blown over them. If the vibration is self-induced then the frequency of "flutter" will fall somewhere between the first bending and second bending mode since the flutter will more than likely
be a coalescence type flutter for a system with a low
mass ratio as this one has. I would check the second mode frequency...if the vibration frequency of the string falls between the first and second modes you probably have a self-excited type vibration.