You have to make clear which vibrations you mean: is it when you are starting driving and the clutch is not fully engaged? Than it could be acceleartion judder where the wheels are getting into a stick-slip effect. This has nothing to do with the clutch.

Or do you mean in idle. Than the vibration of the engine is transmitted to the gearbox and it can lead to vibrations in the gearbox (loose gears vibrate). Or if you donot use a two mass flywheel the vibrations of the engine can be transmitted to the gearbox.

So it depends.

Dear markus,

I mean the vibrations which happens when you start driving with low acceleration which tires slipping don't happen, but the facing rivets of the clutch's disk is not fully engaged to the pressure plate. In these situations there's parameters which causes vibrations that driver completely feels these vibrations and it causes discomfort of driving in cars.

I think that the second type of the vibration you mentioned which causes rattle noise of the gearbox refers to pre-damper clutches and dual mass flywheels that damps the almost regular vibrations of the engine.

I think you're referring to something called "clutch chatter," or "grabbing," in English. This is caused by uneven slippage while the clutch is being engaged. And it then disappears when the clutch is fully engaged, assuming of course there isn't also clutch slippage going on.

http://www.freeasestudyguides.com/manual-transmission-clutch-chatter.html

There are probably many degrees of this, from small and perhaps "unavoidable," to severe. I think that when chatter becomes very noticeable with relatively new clutch, it's probably mostly caused either by foreign matter on the clutch plates, or because the clutch has been overheated by being slipped too much, engine revving too high while engaging the clutch, or maybe if the linkage wasn't adjusted correctly, causing some amount of slight slippage for a long time.

You're absolutely right that this gives a bad feeling to the driver. Nothing like a smooth-engaging clutch. Just like brakes, you want the clutch faces to engage without any amount of grabbing.

Dear albert,

you are correct.. i exactly mean clutch chatter especially the one happens in the beginning of the motion. in addition to facing rivets temperature you mentioned, i think that static and dynamic stiffness coefficient of bellviles and cushion rivets matter too much in this occurrence.

Hamid, you might want to start with these references. The authors used finite element analysis to determine the critical design parameters for different clutch applications.

http://machinedesign.com/fea-and-simulation/finite-element-analysis-reveals-clutch-vibrations

As you might expect, there's no single best design. The link gives just a brief overview. The important part is the two references.

i totally agree with the views expressed by Dr. Albert Manfredi. Added to that there are cengrifugal forces casuing vibrations if there is small misalignment between the shafts.   

Dear Krishna

I don't think that it would be any misalignment between shafts in clutch and drive line system generally.

And about centrifugal forces ... what forces do you mean exactly in this issue ?

The word "clutch chatter' is to be used in stead of vibration, because virbration is general term associated wih many reasons. When engine shaft is coupled wih shaft of dynamometer, there may be vibrations due to misalighement of shafts.