.Damping is a crucial parameter for musical instrument sounds. The damping of wood for guitars or pianos or of leather or mylar for percussion instruments is often heavily damped. Next to the damping caused by the energy loss due to radiation, an internal damping is using energy and therefore the material stops vibrating fast after it has been struck or plucked.

This internal damping is caused by viscoelastic processes. Here the material is not vibrating perfectly free, but there is a time delay between the force which causes the vibration and the movement of the body.

Viscoelasticity is well known in long term processes. A wooden cupboard might bend down when heavy load is put upon it, and when removing the load the wooden board is still bend. This exists also with guitars which are under tension for a long time by the strings. The wood is ‘flowing’ and the top plate of the guitar is permanently deformed. Contrary, a guitar or piano soundboard glued together with tension looses this tension which cannot be seen from outside.

But there is also a fast viscoelastic force causing the internal damping of wood or leather. This is often very frequency-dependent. Basically, higher frequencies damp out faster than lower ones. But viscoelastic damping work for single frequency bands, therefore making the damping behaviour very frequency dependent. Often it’s this frequency-dependence which give the liveliness to musical instrument sounds.

The cause of viscoelastic damping within the material is still not known. There seem to be a conformational change of molecules which alter their shape and jump from one shape to another when put under tension. But much more research need to be done here.

As internal damping is so important for the instrument sounds, when inventing new material it is crucial to design the internal damping such that the instruments sound interesting.

A Viscoelastic Finite-Difference Time-Domain model is able to perform frequency-dependent internal damping. As it is very time-consuming in terms of calculation it is implemented on a Graphic Processing Unit (GPU), which allows massive parallel processing.

 

Related Publications

Bader, R.: Viscoelastic internal damping finite-difference model for musical instruments physical model sound production. J. Acoust. Soc. Am. 141, 3961, 2017.

Power Point presentation of ASA talk 2017:

Viscoelastic internal damping