Claudio Pedrazzi

Hi

It all very much depends.

If damping is low as for steel, say, in the region of a structural loss factor in the range 5E-4 to 5E-5, then sound radiation matters as it tends to be in the range 1E-3, ie it then matters as it is the stronger phenomenon.

Yes, sound radiation is affected by shape but this is not its greatest driver as boundary condition or your sensor cables can transmit as much power and hence add ‘damping’.

However, if your material damping is high and it works the same way between two setups then it is easier to transfer values.

A cylinder and a plate behave quite differently though, so what you get for a plate does not necessarily apply for a cylinder.

But, it is not about shape as such. It is not a material question either. That too is overly simplified.

To give you an idea.

Imagine a dashpot damper. Let’s assume it is designed such that it magically provides 100 % damping wrt to its Input Power.

If you hook it to the position on you structure with the highest vibration amplitude, say it is a simply supported plate and the first mode, so you connect it to the plate centre position with the damper connected to ground. Voila - you get super high damping for this mode,

However, the next mode will have its nodal point at this position and it will be poorly damped as a result.

Similarly, if you again consider the first mode and keep the connection point but align the damper parallel with the plate, you will again have poor damping as the damper is not loaded.

To continue, add an identical plate and hook the other damper end to the middle section of the plate. Will it be twice as good? Yes and No as the plates will now have two modes, one in which the move out of phase and highly load the damper, as intended, and a second combo where they move in phase and hardly load it at all.

And, of course, you have the situation of the first case where you leave the damper free to move instead of honking it to the ground. Then the damper cannot add damping to the plate.

If you consider liquid loading on the plate. Vibration amplitude will be greatly reduced as the liquid is much heavier than air. Is the plate more damped? Probably not, as sound radiation into water tends to be lower than into air. What happened was that mass was added to the plate which reduced amplitude. This is not damping, though many like to call it that.

Damping is the destruction of vibration energy into heat. A nearly irreversible process.

Only, there are situations where a feedback may occur from damping mechanisms. Break squeal is one such. Then you have negative damping, ie generation of power, as the squeal feeds off from the wheel rotation.

So, there really is no simple answer to your question.

There are rules of thumb, some general recommendations. However, on the topic of damping, there is mostly lots of confusion.

Damping or the damn-d thing...

At least for ortotropic materials it is. e.g wood. The crossgrain damping is higher than the along grain damping. If the mode shape is predominantly bending across grain, it will be more damped than modes mainly with nodal lines and bending in the lowest damping direction.

A solid object is also to some extent like a room. If you change the room shape and dimension, the damping will change as well, at least so in the higher frequencies.

In many applications, damping is highly dependant on the boudary conditions and friction in contact, as well as fluid object contact and radiation.

For wood plates Woodhouse and McIntyre showed that even the thickness distribution of a wooden plate can influence the damping of each mode. If the surface is smooth, it will be less damped, as far as I can rememeber. They line out the theory and I do think it can be modified to be valid for isotropic plates.

For a 3D object i am less sure. But one may see given mode shapes be more supressed for given object shapes. Then higher damping may appear. In general damping is a frequency- and shape dependant nonlocal property.

Hi

I don't want to demote or overcomplicate.

Unfortunately, most damping models run on crutches but they are what we have and must work with and, absolutely correct Claudio Pedrazzi

There is interesting work being made by violin aficionados like https://www.researchgate.net/profile/Jim-Woodhouse that https://www.researchgate.net/profile/Anders-Buen mention. Also, Prof https://www.researchgate.net/profile/Janko-Slavic group has made some interesting work using first principles to calculate damping as thermal waves - which makes a lot of sense for many materials.

We'll get a breakthrough sooner or later which will turn this from a session with swirling of tea leaves/a reading of fish intestine into actual science based on first principles.

/C

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