Equation for transmissibility estimation

[bgoo]

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.

 

[GregLocock]

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

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[bgoo]

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,

 

[tomirvine]

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

http://www.vibrationdata.com