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# Damping Coefficient

## Damping Coefficient

(OP)
I am currently involved in analysing dynamic effects (shock,vibration) using Pro Mechanica as my calculation tool. During the setup of the analyses I am being asked to input a % Damping coefficent for the material/material combination under test. Is anyone aware of literature detailing this data for different materials or failing this a method for calculating the value.

### RE: Damping Coefficient

Longer answer: it is not calculable with any great reliability. We have modelling packages (VSIGN) that do model discrete damping elements and can combine FE results into a non linear model to give estimates of the overall system response.

If you are looking at fairly simple structures then a test for the damping of the materials may help.

The other option is to get an experimental modal analysis of a similar system and use the damping values extracted from that for your modes. This is what we do typically.

Damping coefficients for say a steel crankshaft can be as low as .001, altough .01-.02 is more typical. For cast iron blocks with a few bolted joints maybe use .05

If you do a modal on an entire vehicle then the damping can be as high as .1, even if the shock absorbers etc have been removed. We'd tend to ignore any modes with damping higher than that as our estimates of their parameters would be so poor.

There is some literature on this - the machine tool design people are keen to improve their understanding of the tool/part interface, which is obviously heavily non-linear, but I don't have any paper numbers. The papers I see about this are usually from the International Modal Analysis Conference, but I have no contact info for them.

Cheers

Greg Locock

### RE: Damping Coefficient

I am a little confused. You say that you are being asked to enter a % damping coefficient as part of the material definition.

When damping is expressed as a percentage it usually implies that the quantity is the "Critical damping ratio". This is (usually) a measure of the damping for each mode of vibration of the structure rather than a material property. For a material property, it is more likely to be a loss factor, but I have never seen these written as percentages (Although I have seen them expressed in dB so it's possible!).

The inherent damping in the material is often the least important source of damping in a sructure. Damping at connections, attatchments etc. and damping by acoustic radiation are often much higher. For example: I have recently been developing new ways of measuring modal damping and two of the simple structures I have been looking at are a flat rectangular aluminium plate and an identically sized aluminium plate which is divided into 4 quarters by aluminium stiffeners.

Critical damping ratios for the first 10 or so modes range from 0.04% to 0.8%. For the stiffened plate, they vary from 0.5% to 2% even though aluminium is used throughout.

I understand that in Pro Mechanica it is possible to specify critical damping ratio on mode-by-mode basis. This is a major improvement on many other FE packages where unsuitably simple damping models (usually Rayleigh damping) are used. Like Greg says, the usual approach is to measure modal damping and then put those results into your model. Of course this strictly only works for linear viscous damping and does not allow for damping coupling between modes.

M

PS: Greg can you clarify the units for the values you quoted? Are they loss factors or percent loss factors or critical damping ratios or percent critical damping ratios?

### RE: Damping Coefficient

They are the numbers that we put into the table!

Hmm, well that wasn't very helpful.

They are proportion of critical damping, so in the more useful %age form that's 0.1% as a minimum up to 10% where the peaks get so broad as to make estimation unreliable. I'll emphasis that those figures are for automotive components and assemblies.

I can easily believe .04% for pure cantilevers and the like. The difference in damping you've made by welding in stiffners is VERY interesting - what's the damping mechanism?

Cheers

Greg Locock

### RE: Damping Coefficient

Hi Greg

They are not welded, they are bolted at 20 mm intervals so It's most likely friction combined with bending of the bolts (though the mode shapes are the same as the fe prediction for a continuous connection though.

The panel is about 500x800x5 mm and the stiffeners are 12 mm wide x 50 mm deep. The stiffeners are positioned all around the the edge of the plate and across the centre.

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The whole thing is freely suspended.

The interesting thing about this structure is that the the first 4 modes and the 9th mode which are very similar to the free flat plate mode shapes (overall torsion and bending etc) have consistently low modal damping (0.5%). Modes 5 to 8 are the first group of modes where stiffeners remain stationary and the individual subpanels behave as plates with clamped boundary conditions, moving in phase or in antiphase with each other (See below). These modes have damping ratios which range from 1.5 to 2 %.

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There is no way that a damping model such as "equal modal damping per mode" or Rayleigh damping (alpha*M + beta*K) could adequately represent this behaviour.

I have a paper coming out on this matter in Journal of Sound and Vibration (it includes the work carried out on this structure, but with constrained laher damping treatment added to one of the sub-panels to make modes 5 and 6 non-proportionally damped). So keep a look out for it.

M

### RE: Damping Coefficient

So I'd guess that the high bending strains at the bolted connections set up some sort of friction damping. I was hoping you were going to say you'd welded it.

Cheers

Greg Locock

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