Real-time implementation of a friction drum inspired instrument using finite difference schemes

Physical modelling sound synthesis is a powerful method for constructing virtual instruments aiming to mimic the sound of real-world counterparts, while allowing for the possibility of engaging with these instruments in ways which may be impossible in person. Such a case is explored in this paper: particularly the simulation of a friction drum inspired instrument. It is an instrument played by causing the membrane of a drum head to vibrate via friction. This involves rubbing the membrane via a stick or a cord attached to its center, with the induced vibrations being transferred to the air inside a sound box.
This paper describes the development of a real-time audio application which models such an instrument as a bowed membrane connected to an acoustic tube. This is done by means of a numerical simulation using finite-difference time-domain (FDTD) methods in which the excitation, whose position is free to change in real-time, is modelled by a highly non-linear elasto-plastic friction model. Additionally, the virtual instrument allows for dynamically modifying physical parameters of the model, thereby allowing the user to generate new and interesting sounds that go beyond a real-world friction drum.