TY - JOUR
T1 - A Hamiltonian approach to simulation of acoustic systems involving nonlinear interactions
AU - Chatziioannou, Vasileios
AU - van Walstijn, Maarten
PY - 2013/11
Y1 - 2013/11
N2 - Nonlinear interactions take place in most systems that arise in music acoustics, usually as a result of player-instrument coupling. Several time-stepping methods exist for the numerical simulation of such systems. These methods generally involve the discretization of the Newtonian description of the system. However, it is not always possible to prove the stability of the resulting algorithms, especially when dealing with systems where the underlying force is a non-analytic function of the phase space variables. On the other hand, if the discretization is carried out on the Hamiltonian description of the system, it is possible to prove the stability of the derived numerical schemes. This Hamiltonian approach is applied to a series of test models of single or multiple nonlinear collisions and the energetic properties of the derived schemes are discussed. After establishing that the schemes respect the principle of conservation of energy, a nonlinear single-reed model is formulated and coupled to a digital bore, in order to synthesize clarinet-like sounds.
AB - Nonlinear interactions take place in most systems that arise in music acoustics, usually as a result of player-instrument coupling. Several time-stepping methods exist for the numerical simulation of such systems. These methods generally involve the discretization of the Newtonian description of the system. However, it is not always possible to prove the stability of the resulting algorithms, especially when dealing with systems where the underlying force is a non-analytic function of the phase space variables. On the other hand, if the discretization is carried out on the Hamiltonian description of the system, it is possible to prove the stability of the derived numerical schemes. This Hamiltonian approach is applied to a series of test models of single or multiple nonlinear collisions and the energetic properties of the derived schemes are discussed. After establishing that the schemes respect the principle of conservation of energy, a nonlinear single-reed model is formulated and coupled to a digital bore, in order to synthesize clarinet-like sounds.
U2 - 10.1121/1.4831494
DO - 10.1121/1.4831494
M3 - Article
C2 - 24181826
VL - 134
SP - 4219
JO - Journal of the Acoustical Society of America
JF - Journal of the Acoustical Society of America
SN - 0001-4966
IS - 5
ER -