A modal-based approach to the nonlinear vibration of strings against a unilateral obstacle: Simulations and experiments in the pointwise case

Clara Issanchou (1) , Stefan Bilbao (2) , Jean-Loic Le Carrou (1) , Cyril Touzé (3, 4) , Olivier Doaré (3, 4)

1 IJLRDA-LAM - Lutheries - Acoustique - Musique
2 Acoustics and Audio Group
3 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles
4 DFA - Dynamique des Fluides et Acoustique

This article is concerned with the vibration of a stiff linear string in the presence of a rigid obstacle. A numerical method for unilateral and arbitrary-shaped obstacles is developed, based on a modal approach in order to take into account the frequency dependence of losses in strings. The contact force of the barrier interaction is treated using a penalty approach, while a conservative scheme is derived for time integration, in order to ensure long-term numerical stability. In this way, the linear behaviour of the string when not in contact with the barrier can be controlled via a mode by mode fitting, so that the model is particularly well suited for comparisons with experiments. An experimental configuration is used with a point obstacle either centered or near an extremity of the string. In this latter case, such a pointwise obstruction approximates the end condition found in the tanpura, an Indian stringed instrument. The second polarisation of the string is also analysed and included in the model. Numerical results are compared against experiments, showing good accuracy over a long time scale.

Mots clés: Experimental study; 3D string vibration; Numerical methods; Unilateral contact; Sound synthesis; Tanpura

Mots clés: approche modale; Corde vibrante; schéma conservatif; synthèse sonore; contact unilatéral

Domaines: Acoustique [physics.class-ph]; Analyse numérique [math.NA]; Vibrations [physics.class-ph]

Clara Issanchou, Stefan Bilbao, Jean-Loic Le Carrou, Cyril Touzé, Olivier Doaré. A modal-based approach to the nonlinear vibration of strings against a unilateral obstacle: Simulations and experiments in the pointwise case. Journal of Sound and Vibration, 2017, 393, pp.229-251. ⟨10.1016/j.jsv.2016.12.025⟩. ⟨hal-01461730⟩