Nonsmooth contact dynamics for the numerical simulation of collisions in musical string instruments

Clara Issanchou 1 Vincent Acary 2 Franck Pérignon 3 Cyril Touzé 1 Jean-Loic Le Carrou 4
1 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles
2 TRIPOP - Modélisation, simulation et commande des systèmes dynamiques non lisses
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann
3 LJK - Laboratoire Jean Kuntzmann
4 DALEMBERT - Institut Jean Le Rond d'Alembert
Abstract : Collisions in musical string instruments play a fundamental role in explaining the sound production in various instruments such as sitars, tanpuras and electric basses. Contacts occuring during the vibration provide a nonlinear effect which shapes a specific tone due to energy transfers and enriches the hearing experience. As such, they must be carefully simulated for the purpose of physically-based sound synthesis. Most of the numerical methods presented in the literature rely on a compliant modeling of the contact force between the string and the obstacle. In this contribution, numerical methods from nonsmooth contact dynamics are used to integrate the problem in time. A Moreau-Jean time-stepping scheme is combined with an exact scheme for phases with no contact, thus controlling the numerical dispersion. Results for a two-point bridge mimicking a tanpura and an electric bass are presented, showing the ability of the method to deal efficiently with such problems while invoking, as compared to a compliant approach, less modelling parameters and a reduced computational burden.
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Clara Issanchou, Vincent Acary, Franck Pérignon, Cyril Touzé, Jean-Loic Le Carrou. Nonsmooth contact dynamics for the numerical simulation of collisions in musical string instruments. Journal of the Acoustical Society of America, Acoustical Society of America, 2018, 143 (5), pp.1-13. ⟨10.1121/1.5039740 ⟩. ⟨hal-01806133v2⟩

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