Percussion Instrument Modelling In 3D: Sound Synthesis Through Time Domain Numerical Simulation
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Ch. 5 - Coupling with the acoustic field in 3D
The 3D wave equation for the acoustic field is the main
subject of this chapter. The basic equations in terms of an acoustic velocity
potential are first discussed in the lossless case. Then, the numerical
discretisation of this model is performed. The core of the chapter deals with
embeddings, that is the coupling between 2D structures and the 3D field. After
describing the simple case of a linear membrane, air coupling is extended to
several different systems, including Berger nonlinearity, von Kármán
nonlinearity, the mallet/membrane collision and the string/membrane collisions.
Air coupling in the presence of von Kármán nonlinearity and collisions is one
of the contributions of this work.