Vibration Attenuation

[likearock]

I have been pondering on something all day and have been unable to track down any helpful literature on my particular problem. Suppose for the sake of simplicity you have an infinitely long steel cylindrical rod (say 5" in diameter)suspended in a vacuum (or neglecting all interaction with the surroundings). Now suppose one end of this rod is struck creating a shock/vibrational wave with a known amplitude at Xn and known corresponding harmonic amplitudes at Xn as well as the frequency. Is there a way to theoretically calculate the attenuation of said wave or corresponding amplitude of said wave after traveling distances of Xn+1, Xn+2, etc. I assume this would have to be related to some type of attenuation coefficient of steel (which I can't find). Particularly I'm interested in the reading I would see from an accelerometer placed 1 m from the wave point of origin vs. say 2000m from the point of origin. Whats your thoughts?

 

[IRstuff]

perhaps here:

http://www.cs.wright.edu/~jslater/SDTCOutreachWebsite/damping properties of materials.pdf

TTFN
faq731-376

 

[tygerdawg]

The answer is YES. Unfortunately, the last time I did something like this was in my graduate-level Advanced Vibrations class in the mid-80's. So I can't recall exactly.

I do remember that it was required to model the physical body using some form of three-dimensional equation of motion formula, for the most-useful coordinate system. This formula was a monster with many terms, used the "del" operator (inverted triangle), and expanded into partial differential equations across three coordinate system variables. In your case the most likely coordinate system would be cylindrical. Luckily, all us grad students were shown that through juidicious selection of coordinate systems and other "minimum-impact" or "higher-frequency component" variables of the problem, one could take a hatchet to the expanded formula and delete many terms. That made it all easier. The more advanced "real-world" problems would require computational solutions because analytical solutions were not possible to achieve.

The stereotypical homework application for this class was vibrational boundary analysis of an infinite plate with a point source of excitation. The goal of the equation of motion derivation was to determine the response to the excitation of the infinite plate at any arbitrary location. It was based on the professor's research. Since our professor was swimming in Reagan-era defense-fed research programs, we smart-@ss students figured out the application for this research: submarine hulls getting ping-ed by enemy sonar.

"Attenuation", you say? This would involve wave-propagation components in the equation of motion, coupled with material property values.

TygerDawg
Blue Technik LLC
Virtuoso Robotics Engineering

http://www.bluetechnik.com

 

[likearock]

I can certainly model the system in terms of its harmonic motion after a mass, spring, and damper in the form of X(t)= Ae^w(sin(wdt)). However this does not describe the decay of one impulse traveling through the rod over a very long distance. For instance if I know the amplitude and frequency of the resulting wave at a distance of 5m from the excitation how could I predict the amplitude at a distance of 5000m?

 

[jmw]

I think that the most important parameter is likely to be frequency.
Low frequency attenuates less than high. This is why low frequency devices are very vulnerable to plant vibration, much of which is generated at mains frequencies.



JMW

http://www.ViscoAnalyser.com

 

[FeX32]

Yes there is a way analytically. I have done something simular before (also in grad school)

You need to solve the PDE that governs its motion. You have said null about boundary conditions except that it is infinitely long. Constraints? See Continuous systems or Distributed systems in

http://www.mech.eng.unimelb.edu.au/dynamics/14lec.pdf

I hope you remember how to solve a PDE

You can start with the String equation assuming it's a 1D vibration. Then move on to the 4th order Beam equation. By solving the relation you will end up with a solution for its motion, frequencies (n=1 to infinity) and an approximate attenuation (through damping)

If I had more time I would help solve.





Fe (IronX32)

 

[GregLocock]

Or steely minded friend raised the issue I was interested in - flexural waves or axial?

Either way the analysis is going to rely on solving a wave eqaution, or looking it up in a book, since it is a pretty well known problem.

The flexural solution is far more interesting and complex.



Cheers

Greg Locock


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[handleman]

The unanswered question here is how to find the end of an infinitely long cylinder so you can hit it with your hammer...

-handleman, CSWP (The new, easy test)

 

[GregLocock]

Tell an apprentice to go and find it.

Cheers

Greg Locock


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