LNT audio group Physical modeling of membranes using multidimensional transfer functions

Description of membrane vibrations by PDEs

Membrane vibrations are in contrast to string vibrations three dimensional problems. They depend on one temporal variable and on two spatial demensions. Analyzing the memebrane with the basic laws of physics leads to a partial differential equation containing temporal and spatial derivatives. With initial and boundary conditions it has a definite solution. This solution cannot be implemented directly in the computer due to the differential operators.

Functional transformation method

As other methods the functional transformation method (FTM) discretizes the PDEs for computer implementation. With the same steps as for two dimensional problems (as described in string vibrations), a time and space discrete solution is derived from a multidimensional transfer function model.

Sound Examples

Sounds of vibrating membranes produced with the functional transformation method give an impression of the possibilities of this method.

Kettle drum,
Tom high,
Tom low,
metal drum high,
metal drum low.

Implementation for a vibrating membrane

A visualization of a vibrating membrane can be downloaded from this site.
 

Publications on membrane synthesis with FTM

In the following there is a list of publications dealing with membrane synthesis based on FTM. There the functional transformations are described in detail and they are explained on transversal vibrating, disperive membrane with frequency dependent losses.
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L. Trautmann, S. Petrausch, R. Rabenstein
Physical Modeling of Drums by Transfer Function Methods
In Proc. Int. Conf. on Acoustics, Speech & Signal Processing (ICASSP), IEEE, Salt Lake City, Utah, May, 2001.
Lutz Trautmann
Last modified: Mon Jul 9 10:01:35 MET 2001