Subject: Sub harmonic vibrations – In a thin steel ring?

I've googled around and can't find much on sub harmonics.

I turned a thin steel ring from a pipe on a lathe at work. The ring is about 8 
½ cm in diameter, about 4mm thick, and about 4mm wide.

The speed of sound in steel is about 6000 meters per second.

I was wondering if I could induce sub harmonic resonant vibrations in this 
steel ring. 

My plan was to suspend the ring via a magnetic suspension, and then to excite 
it with a small electromagnet at some sub harmonic frequency (say, at 1/2 the 
fundamental, ~ 11 kHz). Record the sound coming from the ring, and perform an 
FFT on the recording to get a frequency power spectrum. However, I was never 
able to fabricate a magnetic suspension system which could “float” my ring. 

The path length of my ring is approx: c = pi * d ~ 27cm = 3.14 * 8.5cm.
At 6000 meters per second, my fundamental frequency should be close to: 
6000m/sec / 0.27m = ~ 22 kHz.

As different from a “stretched string” supported at two end points, in which 
case there are no frequencies smaller than the fundamental. I suspect that I 
should get not only integer multiples of the fundamental, but because the 
system has no end points, also fractional harmonics – 1/2, 1/3, 1/4…


I can “tap” the ring and hear frequencies that I know are less than 22 kHz. 

My question is: “Does anyone know if I should get sub harmonic resonant 
vibrations in such an experiment?”

Thanks much in advance,

~Randy

Re: Sub harmonic vibrations – In a thin steel ring?