Contact problems with friction applied to musical sound synthesis

Abstract

Modalys, a sound synthesis software developed at Ircam for research and musical applications, allows one to build virtual instruments based on physical models to obtain the most entire range of expressive variations in the instrument in response to intuitive controls. An instrument, as a complex structure, is described by the mechanical/acoustical interaction of its components (strings, tubes, resonators, soundboard,...). Some new research has been done recently to extend the sound prediction to three‐dimensional objects with the help of numerical methods. In particular, theoretical and numerical treatment of the unilateral dynamic contact with friction between two arbitrary elastic bodies is studied. In addition to the classical variational statement that arises from static problems, a dynamic contact condition is needed and found by adjusting the energy balance law to the impenetrability condition. In the context of infinitesimal deformation, a reciprocal formulation is then used to reduce this well‐posed problem to one involving Green functions defined only on contact surfaces. This allows us to use considerably fewer unknowns compared to finite difference algorithms. The ability of the method to predict the contact interaction between two elastic bodies, irrespective of the material constitution and geometry, is highlighted by analytical and numerical simulations.