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Equation for transmissibility estimation

Equation for transmissibility estimation

Equation for transmissibility estimation

(OP)
Folks, Anybody have a good equation to estimate the transmissibility of the cylinder along the axis?  (In my application, the cylinder is hanging vertically downward). Steinberg used the equation Q = 2 sqrt(fn) in some of his examples to estimate the transmissibility of beam structure.  But I suspect the Q is orientation dependent and my not be applicale to my case.

Anywhere I can find of good collection of equation for estimating transmissibility of different structure?

Note;  fn is resonance frequency

Thanks.

RE: Equation for transmissibility estimation

Can you define transmissibility, in your context? I don't see how it can be a single number for a start.

Cheers

Greg Locock

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RE: Equation for transmissibility estimation

(OP)
Greg,

The tramissibility (Q) is simple the ratio of maximum output force to the maximum input force on a structure during vibration. At resonance, Q can be very high.  Steinberg indicated that the force is proportion to square root of natural frequency of the structure.

Regards,

RE: Equation for transmissibility estimation

The quick answer is that you need to a finite element analysis combined with modal testing.

Here is a longer answer...

Q is the transmissibility at resonance, preferably for a single-degree-of-freedom system.

Q is related to the damping ratio.  The damping must be measured for a given test item including its boundary condition.  

Damping cannot be calculated using analytical formulas.  Empirical damping formulas are questionable.

Furthermore, the response of a continuous structure or even a multi-degree-of-freedom system depends on eigenvectors, effective modal mass values, modal participations factors, as well as on the modal damping.

Cylinders are surprisingly complicated.  A cylinder has two equations of motion, which include both bending and membrane response.  These equations do not even include longitudinal or torsional motion.

I have posted a paper at:

http://www.vibrationdata.com/tutorials2/infinite_cylinder.pdf

 
Tom Irvine
www.vibrationdata.com

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