Alberto Torin

This work is concerned with the numerical simulation of percussion instruments based on physical principles. Three novel modular environments for sound synthesis are presented: a system composed of various plates vibrating under nonlinear conditions, a model for a nonlinear double membrane drum and a snare drum. All are embedded in a 3D acoustic environment. The approach adopted is based on the finite difference method, and extends recent results in the field. Starting from simple models, the modular instruments can be created by combining different components in order to obtain virtual environments with increasing complexity. The resulting numerical codes can be used by composers and musicians to create music by specifying the parameters and a score for the systems. Stability is a major concern in numerical simulation. In this work, energy techniques are employed in order to guarantee the stability of the numerical schemes for the virtual instruments, by imposing suitable coupling conditions between the various components of the system.

Before presenting the virtual instruments, the various components are individually analysed. Plates are the main elements of the multiple plate system, and they represent the first approximation to the simulation of gongs and cymbals. Similarly to plates, membranes are important in the simulation of drums. Linear and nonlinear plate/membrane vibration is thus the starting point of this work. An important aspect of percussion instruments is the modelling of collisions. A novel approach based on penalty methods is adopted here to describe lumped collisions with a mallet and distributed collisions with a string in the case of a membrane. Another point discussed in the present work is the coupling between 2D structures like plates and membranes with the 3D acoustic field, in order to obtain an integrated system. It is demonstrated how the air coupling can be implemented when nonlinearities and collisions are present. Finally, some attention is devoted to the experimental validation of the numerical simulation in the case of tom tom drums. Preliminary results comparing different types of nonlinear models for membrane vibration are presented.