How can a part's geometry be used for damping or to reduce vibration?

[506818]

Hi,

So basically I am wondering how can you increase damping within a part, just by altering its geometry. I've researched this topic, but haven't yet found anything significant. Here are my main findings:

- Rayleigh Damping uses the equation: [C] = α[M] + β[K], which to me shows that mass and stiffness affect damping
- Damping constants are difficult to obtain; use of available literature and experimentation are the only ways to go

From this, I believe there is a useful link between stiffness and damping, and that I could design a part in certain ways to increase damping/reduce vibration (I understand these are very different things). For example, would stiffening a part, reduce the response of the part under excitation?

The aim for me is to develop an understanding from a design perspective as to how we can use geometry to reduce stresses in a part under dynamic loading.

Thanks in advance for any help.

 

[ptsal]

Hey,

We have to understand what you really want to do.

When you design a system that would be under any dynamic loading you have first of all, from my understanding, design it so that the structural modes (and there natural frequencies) are far from the dynamic load's frequency. When that's not possible or difficult to accomplish, you then have to start thinking on damping systems to reduced the energy transmited, and therefore stresses due to the "movement", to the part or system.

So before you think of stiffening a structure you have to know the dynamic behaviour of all the parts involved, including the source of the load(frequency, Load, direction, etc). With all those elements you are capable of designing a system that is less prone to become damaged.

Hope I could help. But I believe there are people more qualified that can clarify you.

 

[ronfrend]

Hi 1Muffin,

Are you trying to increase damping or change the natural frequency?
The natural frequency of a beam is 1/2π x (EI/μL^4)
where E - Youngs modulus
I - polar moment of interia
μ - mass per unit length
L - length of beam

Take E and I together you get stiffness
Take μ and L together and you get mass.

So if you increase the stiffness you increase the natural frequency. If you increase the mass you lower the natural frequency.

Changing the damping is more complex. By increasing stiffness you will get a smaller amplitude of vibration for a given excitation force but you also need to consider that the damping ratio is the damping (in kg/s) divided by 2(m k)^0.5.
Where
c is the damping
m is the equivalent mass and
k is the equivalent spring constant.

(I dug this out from one of my old text books - SCHAUM's Mechanical Vibrations - 1996)

I hope I didn't make this more confusing

Ron


Ron Frend

http://www.predicon.net

 

[GregLocock]

I suggest you go back to a single degree of freedom spring/mass/damper model to test your theories.

Yes you can often reduce the amplitude of vibrations by making the part stiffer, but sometimes you'll make it worse. That depends on the excitation spectrum.



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[BrianE22]

Getting parts to rub on each other would help increase damping. That rubbing and wear may cause other problems though. You might also want to take a look at "damping coatings".

On the material end, I don't know why, but aluminum is not very self-damping. Cast iron is used for machine tool bases in large part due to its damping properties.

 

[PJeram]

Howdy,

My first post to this forum.

Your first and last lines pose 2 very different questions. 1. 'to increase the damping' and 2. 'to reduce stresses under dynamic loading'; both by altering a parts geometry.

As already mentioned, damping and stiffness are very different things. Imagine twanging a plastic ruler on the edge of the desk, for a fixed length, the ruler will vibrate at a fixed frequency which is determined largely by the stiffness of the material and the geometry of the ruler design. The amount of time for which the ruler continues to vibrate is determined largely by the internal damping in the material from which the ruler is made.

The aforementioned features that rub together have been used to reduce vibrations in car door mirrors for decades, but this could be construed as going beyond changing the geometry, because you are introducing a fit condition that would require assembly.

The only way I can think of to affect the damping in a single, as-cast/as-moulded/as-machined component by changing its geometry is to have a suitably large mass or 'lump' of the material incorporated into the design, and suspended by relatively flexible spring features that allow this lump to vibrate somewhat independently of the main component. The geometry and location of the lump and spring features could then be independently tweaked to damp the resonant frequencies of the main component (a little like the 'brick' that is fixed inside some washine machines to reduce the vibrations at spin; a crude solution with mass and cost penalties, but cheap and indicative of the difficulty in damping the machine in more mass/cost efficient ways).

I'd be interested to hear thoughts on this and whether this helped.

Regards,

Paul.